If the sum of first 7 terms and 15 terms of an A.P. are 98 and 390 res

1.	If the sum of first 7 terms and 15 terms of an A.P. are 98 and 390 respectively, then find the sum of first 10 terms.
Answer» 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

If the sum of first 7 terms and 15 terms of an A.P. are 98 and 390 respectively, then find the sum of first 10 terms.

Answer»

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