Question

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.​

Answer 1

$\huge\sf\pink{Required \: \: Answer}$

To Solve:

find the difference between the sums of their first 50 terms.

Given:

• first terms of these APs be 3 and 8.
• Same Common Difference.

Solⁿ:

a¹ = 3

a'¹ = 8

S⁵⁰ - S'⁵⁰ = Common Difference

${s}^{n} = \frac{n}{2 } (2a(n - 1)d)$

$= [ \frac{50}{2} ( 2 × 8 + ( 50 - 1 )d ] \: - \: [ \frac{50}{2} ( 2 × 3 + ( 50 - 1 )d ]$

$= [ 25 ( 16 + 49d ) ] - [ 25 ( 6 + 49d ]$

$= [ 400 + 1225d ] - [ 150 + 1225d ]$

$= 400 + 1225d - 150 - 1225d$

$= 400 - 150$

${ \boxed{ \pink{= 250}}}$

Hence, 250 is the difference between the sum of their first 50 terms.

HOPE IT HELPS

MARK BRAINLIEST PLS :)