Sum of the first 7 terms of AP = 98
\(\frac{7}{2}\)[2a + (7-1)d] = 98
2a + 6d = 98 × \(\frac{2}{7}\)
2a + 6d = 28
a + 3d = 14 ……………..(1)
Sum of the first 15 terms of AP = 390
\(\frac{15}{2}\) [2a + (15 – 1)d] = 390
2a + 14d = 390 × \(\frac{2}{15}\)
2a + 14d – 52
a + 7d = 26 ……………(2)
by solving (1) and (2)
a = 5 and d = 3
Sum of the first 10 terms 10
= \(\frac{10}{2}\) [2a + (10 – 1)d]
– 5[2(5) + 9(3)]
= 5[10 + 27]
= 5 × 37 = 185