Question 14

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Answer

Let A1, A2, A3, A4, and A5 be five numbers between 8 and 26 such that

8, A1, A2, A3, A4, A5, 26 is an A.P.

Here, *a *= 8, *b *= 26, *n* = 7

Therefore, 26 = 8 + (7 – 1) *d*

⇒ 6*d* = 26 – 8 = 18

⇒ *d *= 3

A1 = *a* + *d* = 8 + 3 = 11

A2 = *a* + 2*d* = 8 + 2 × 3 = 8 + 6 = 14

A3 = *a* + 3*d* = 8 + 3 × 3 = 8 + 9 = 17

A4 = *a* + 4*d *= 8 + 4 × 3 = 8 + 12 = 20

A5 = *a* + 5*d* = 8 + 5 × 3 = 8 + 15 = 23

Thus, the required five numbers between 8 and 26 are 11, 14, 17, 20, and 23.

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

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

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

- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
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.

- Q:-
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:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.

- 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.

- Q:-
A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

- Q:- 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.
- Q:-
Evaluate

- Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.

- Q:-
Find the derivative of x at x = 1.

- Q:-
Using Binomial Theorem, indicate which number is larger (1.1)

^{10000}or 1000. - Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)

- 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.

Ashish Kumar Pathak
2018-12-18 20:17:41

Thank you so much because this solution is given me a hot hint in my mind that help me in solving a lot of problems

Krithik
2018-08-24 19:06:03

Thanks this is very helpful to me Thank u so much

Pawankumar
2018-07-26 15:36:37

Give answer in Hindi

- NCERT Chapter