Question

The sum of the first 10 terms in an arithmetic progression is 50 and the sum of the next 10 terms is 250.Find the 15th term.

Answer 1

Answer:

So 15 th term = 214

Step-by-step explanation :

By using given conditions,

$S_{10}=50\\\\\frac{n}{2} *(2a+(n-1)d)=50\\\\5*(2a+(10-1)d)=50\\\\5*(2a+9d)=50\\\\2a+9d=10 ......(1)\\\\S_{20}-S_{10}=250\\\\=>S_{20}=250+50=300\\\\\frac{20}{2} *(2a+(20-1)d)=300\\\\=>10*(2a+19d)=300\\\\=> 2a+19d=30.....(2)$

(2) - (1) , we get,

$10d=220\\\\=> d = 22$

Sub. d=22 in eq(1), we get,

2 a + 9 ( 22 ) = 10

=> 2 a = -188

=> a = - 94

So 15 th term

$a_{15}=a+14d\\\\=>-94+14(22)\\\\=>-94+308\\\\=> 214$

Hope helps u and mark brainliest