Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms. [CBSE 2011]

Open in App

Solution

Let a₁ and a₂ be the first terms of the two APs.

Here, a₁= 8 and a₂= 3

Suppose d be the common difference of the two APs.

Let $S_{50}$ and $S_{50}^{'}$ denote the sums of their first 50 terms.

$∴ S_{50} - S_{50}^{'} = \frac{50}{2} [2 a_{1} + (50 - 1) d] - \frac{50}{2} [2 a_{2} + (50 - 1) d] = 25 (2 \times 8 + 49 d) - 25 (2 \times 3 + 49 d) = 25 \times (16 - 6) = 250$

Hence, the required difference between the two sums is 250.

Suggest Corrections

Similar questions

Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms.

Q. Two APs have the same common difference. Their first terms are −1 and −8, respectively. The difference between their 4th terms is
(a) −1
(b) −8
(c) 7
(d) −9

Q. Two APs have the same common difference. The first term of one of these is 3, and that of the other is 8. What is the difference between their 2nd terms ?

Q. Two A.P's have the same common difference. If the first term of the two A.P's are

3

and

8

respectively, find the difference between their sum to first

30

terms.

Q. Question 11
Two APs have the same common difference. The first term of one of these is – 1 and that of the other is – 8. The difference between their

4^{t h}

terms is

A) -1
B) -8
C) 7
D) -9

Join BYJU'S Learning Program