Question

if the sum of first 8 terms of an A.P is 136 and that of first 15 terms is 465 then find the sum of first 25 terms​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Sum of first 25 terms is 1275

Step-by-step explanation:

The formula for sum of n terms of an Arithmetic progression is given by

$S_{n}=\frac{n}{2} \cdot [2a + (n-1) \cdot d]$

Sum of first 8 terms is 136, this means $136=S_{8}=\frac{8}{2}\cdot [2a+7d] \implies 2a +7d =34$

Sum of first 15 terms is 465, this means $465=S_{15}=\frac{15}{2}\cdot [2a+14d] \implies a+7d=31$

Solving the both the equations for "a" and "d" we get a=3 and d=4.  Now sum of first 25 terms is given by

$S_{25}=\frac{25}{2} \cdot [ 2a + 24 d] = \frac{25}{2} \cdot [ 2\cdot 3 + 24\cdot 4] =\frac{25}{2}\cdot 51 = 1275$.