Sequence and Series Free CBSE NCERT solution for class 11th mathematics

Q1	Write the first five terms of the sequences whose nth term is a_n=n(n+2)
Q2	Write the first five terms of the sequences whose nth term is \begin{align} a_n = \frac {n}{n+1}\end{align}

Q1	Find the sum of odd integers from 1 to 2001.
Q2	Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
Q3	In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
Q4	How many terms of the A.P. \begin{align} -6, -\frac{11}{2}, -5, ... \end{align} are needed to give the sum –25?
Q5	In an A.P., if pth term is \begin{align} \frac{1}{q} \; and \;qth\; term \; is\; \frac{1}{p}\end{align} , prove that the sum of first pq terms is \begin{align} \frac{1}{2}(pq+1) \; where \; p ≠ q \end{align}
Q6	If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Q7	Find the sum to n terms of the A.P., whose kth term is 5k + 1.
Q8	If the sum of n terms of an A.P. is (pn + qn²), where p and q are constants, find the common difference
Q9	The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms.
Q10	If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
Q11	Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that $a over p open parentheses q minus r close parentheses plus b over q open parentheses r minus p close parentheses plus c over r open parentheses p minus q close parentheses equals 0$
Q12	The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nth term is (2m – 1): (2n – 1).
Q13	If the sum of n terms of an A.P. is 3n² + 5n and its mth term is 164, find the value of m.
Q14	Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Q15	If $fraction numerator a to the power of n plus b to the power of n over denominator a to the power of n minus 1 end exponent plus b to the power of n minus 1 end exponent end fraction$ is the A.M. between a and b, then find the value of n.
Q16	Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)thnumbers is 5:9. Find the value of m.
Q17	A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
Q18	The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

Q1	Find the 20th and nthterms of the G.P. $5 over 2 comma 5 over 4 comma 5 over 8 comma...$
Q2	Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Q3	The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q² = ps.
Q4	The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.
Q5	Which term of the following sequences: $2 comma space 2 square root of 2 comma 4 comma space...$
Q6	For what values of x, the numbers $2 over 7 comma x comma fraction numerator minus 7 over denominator 2 end fraction space$ are in G.P?
Q7	Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 …
Q8	Find the sum to n terms in the geometric progression $square root of 7 space comma space square root of 21 space comma space 3 square root of 7 space comma space...$
Q9	Find the sum to n terms in the geometric progression 1,-a, a²,-a³, ... (if a ≠ -1)
Q10	Find the sum to n terms in the geometric progression x³, x⁵, x⁷ ... (if x ≠ ±1)
Q11	Evaluate $stack sum open parentheses 2 plus 3 to the power of k close parentheses with k equals 1 below and 11 on top$
Q12	The sum of first three terms of a G.P. is $39 over 10$ and their product is 1. Find the common ratio and the terms.
Q13	How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?
Q14	The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
Q15	Given a G.P. with a = 729 and 7th term 64, determine S₇.
Q16	Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.
Q17	If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
Q18	Find the sum to n terms of the sequence, 8, 88, 888, 8888…
Q19	Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, $1 half$ .
Q20	Show that the products of the corresponding terms of the sequences a,ar,ar², ...ar^n-1 and A, AR, AR², ,,,AR^n-1form a G.P, and find the common ratio.
Q21	Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
Q22	If the p^th, q^th and r^th terms of a G.P. are a, b and c, respectively. Prove that a^q-rb^r-pc^p-q=1
Q23	If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P² = (ab)ⁿ.
Q24	Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from $open parentheses n plus 1 close parentheses to the power of t h end exponent space t o space open parentheses 2 n close parentheses to the power of t h end exponent space t e r m space i s space 1 over r to the power of n$
Q25	If a, b, c and d are in G.P. show that $open parentheses a squared plus b squared plus c squared close parentheses open parentheses b squared plus c squared plus d squared close parentheses equals open parentheses a b plus b c plus c d close parentheses squared.$
Q26	Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
Q27	Find the value of n so that $fraction numerator a to the power of n plus 1 end exponent space plus space b to the power of n plus 1 end exponent over denominator a to the power of n space plus space b to the power of n end fraction$ may be the geometric mean between a and b.
Q28	The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio $open parentheses 3 space plus space 2 square root of 2 close parentheses space : space open parentheses 3 minus 2 square root of 2 close parentheses.$
Q29	If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are $A plus-or-minus square root of open parentheses A plus G close parentheses open parentheses A minus G close parentheses end root$ .
Q31	What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
Q32	If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

Q1	Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
Q2	Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
Q3	Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …
Q4	Find the sum to n terms of the series $fraction numerator 1 over denominator 1 cross times 2 end fraction space plus fraction numerator 1 over denominator 2 cross times 3 end fraction space plus space fraction numerator 1 over denominator 3 space cross times space 4 end fraction space plus space...$
Q5	Find the sum to n terms of the series 5² + 6² + 7² + ... + 20²
Q6	Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…
Q7	Find the sum to n terms of the series 1² + (1² + 2²) + (1² + 2² + 3²) + …
Q8	Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).
Q9	Find the sum to n terms of the series whose nth terms is given by n² + 2n
Q10	Find the sum to n terms of the series whose nth terms is given by (2n – 1)²

Q1	Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
Q2	If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Q3	Let the sum of n, 2n, 3n terms of an A.P. be S₁, S₂ and S₃, respectively, show that S₃ = 3 (S₂– S₁)
Q4	Find the sum of all numbers between 200 and 400 which are divisible by 7.
Q5	Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Q6	Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Q7	If f is a function satisfying f(x +y) = f(x) f(y) for all x,y $element of$ N such that f(1) = 3 $sum from x equals 1 to n of space f left parenthesis x right parenthesis space equals space 120$ and , find the value of n.
Q8	The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Q9	The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
Q10	The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
Q11	A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
Q12	The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
Q13	If $fraction numerator a space plus b x over denominator a space minus space b x end fraction space equals space fraction numerator b space plus space c x over denominator b space minus space c x end fraction space equals space fraction numerator c space plus space d x over denominator c space minus d x end fraction space open parentheses x space not equal to 0 close parentheses$ Q14	Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P²Rⁿ = Sⁿ

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

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