Question

The first term of an Ap is - 504 whilethe sum of its 9 terms is-126 findSum of its 30 terms​

Answer 1

Answer:

The sum of its 30 terms is 38167.5

Step-by-step 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:

$S_n = (\frac{n}{2} ) [ 2 a_1 + ( n - 1 ) d ]$

The sum of 9 terms of an AP:

$S_9 = (\frac{9 }{2} ) [ 2(-504) + ( 9 - 1 )d ]$

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

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

(-4536) +36d = -126

36 d = -126+4536

36 d=  4410

$d= \frac{4410}{36}$

d = 122.5

The sum of its 30 terms is

$S_{30} = ( \frac{30 }{2 }) [ 2 (-504) + ( 30-1)(122.5) ]$

$S_{30} =(15) [ 2 (-504) + ( 29)(122.5) ]$

$S_{30} = [ 2 (-504)(15) + ( 29)(122.5)(15) ]$

$S_{30} = [ -15120 + 53287.5 ]$

$s_{30} = 38.167.5$