Question

If the sum of first 7terms and 15terms of an ap are 98 and 390 respectively then find the sum of first 10 terms

Answer 1

Sum of terms in AP=
$n \div 2(2a + (n - 1)d)$
sum of first 7 terms =98
$98 = 7 \div 2(2a + (6)d)$
from that
$14 = a + 3(d)$
let this is first equation

sum of first 15 terms=390

$390 = 15 \div 2(2a + 14d)$
from that
$26 = a + 7d$
let this is second equation

by solving these two equations we get
$d = 3$
$a = 5$
then sum of first 10 terms

$= 10 \div 2((2 \times 5) + (9 \times 3))$
the answer is 185