Question

Find the sum of first 17 terms of an ap whose 4th and 9th terms are -15 and -30 respectively

Answer 1

answer of this question is -612

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assume,

First term be a

Also,

Common difference be d

As we know that,

a(n) = a + (n - 1)d

So,

a(4) = a + 3d = -15 ................. (1)

a(9) = a + 8d = -30 ................. (2)

Now

Subtract (1) & (2),

(a + 8d) - (a + 3d) = -30 - (-15)

5d = - 15

d = -15/5

d = - 3

Now

Using (1) we have,

a + 3d = -15

a + 3(- 3) = - 15

a = -15 + 9

a = - 6

Also,

S(17) = 17/2[2 × (- 6) + (17 - 1) (- 3)]

S(17) = 17/2[-12 + 16 × (- 3)]

S(17) = 17/2[-12 - 48]

S(17) = 17/2[- 60]

S(17) = 17 × (- 30)

S(17) = -510

Therefore,

Sum of 17 terms = -510