Question

The sum of first 9 terms of an AP is zero and its 7th term is 10 find the sum of the first 23 terms ​pls answer fast

Answer 1

Answer:

Let the sum of the first 30 term be S30, first term be a, fourth term be a4 and the sum of first six terms be S6.  

the sum of the first six terms be S6.

Given that S6 = 0 and the fourth term a4 = 2

⇒ a + 3d = 2..........(i)

S6 = 0

n/2(2a + 5d) = 0

⇒ 2a + 5d = 0 .........(ii)

(i) ×2,

2a + 6d = 4...........(iii)

∴ (iii) -  (ii)

∴ d = 4

Substituting the value of d = 4 in (i),

a + 3 ×(4) = 2

⇒ a = 2 - 12 = -10

∴ a30 = a + 29d  

= -10 + 29 × (4)  

= -10 + 116  

= 106  

∴ Sum to first 30 terms = S30 = n/2(a+l)

= 30/2(-10 + 106)

= 15 ×  96

= 1140.

Step-by-step explanation: