Question 1

# Write the first five terms of the sequences whose nth term is a_{n}=n(n+2)

Answer

a_{n} = n(n+2)

Substituting *n* = 1, 2, 3, 4, and 5, we obtain

a_{1} = 1(1+2) = 3

a_{2} = 2(2+2) = 8

a_{3} = 3(3+2) = 15

a_{4} = 4(4+2) = 24

a_{5} = 5(5+2) = 35

Therefore, the required terms are 3, 8, 15, 24, and 35.

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Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

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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.

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How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

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- Q:-
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*n*terms of the series 3 × 8 + 6 × 11 + 9 × 14 +… - Q:- Write the first five terms of the sequences whose nth term is \begin{align} a_n = \frac {n}{n+1}\end{align}
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Find the value of

*n*so that may be the geometric mean between*a*and*b*. - Q:-
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- Q:-
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.

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Name the octants in which the following points lie:

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- Q:-
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.

- Q:-
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.

- Q:-
A die is thrown. Describe the following events:

(i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3

(iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3

Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F’, F’

- Q:-
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.

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