Question

The first term of an Ap is - 504 while

the sum of its 9 terms is-126 find
Sum of its 30 terms​

Answer 1

The sum of its 30 terms is 38167.5

Explanation:

Given:

The First term in the AP is -504

The Sum of its 9 terms is -126

To Find:

The sum of its 30 terms = ?

Solution:

The sum of n terms of an AP:

`S_n = ((n)/(2) ) [ 2 a_1 + ( n - 1 ) d ]`

The sum of 9 terms of an AP:

`S_9 = ((9 )/(2) ) [ 2(-504) + ( 9 - 1 )d ]`

`S_9 = (4.5 )[ 2 (-504)+ ( 8 ) d ]`

`(4.5 )(2)(-504) + (4.5) 8 d = - 126`

(-4536) +36d = -126

36 d = -126+4536

36 d= 4410

`d= (4410)/(36)`

d = 122.5

The sum of its 30 terms is

`S_(30) = ( (30 )/(2 )) [ 2 (-504) + ( 30-1)(122.5) ]`

`S_(30) =(15) [ 2 (-504) + ( 29)(122.5) ]`

`S_(30) = [ 2 (-504)(15) + ( 29)(122.5)(15) ]`

`S_(30) = [ -15120 + 53287.5 ]`

`s_(30) = 38.167.5`