Question

the sum of first six terms of an AP is zero and the fourth term is 2. find the sum of its First 30 terms ​

Answer 1

Answer:

Hope it is helpful to you...

Answer 2

Sn = n/2 { 2a+(n-1)d }

given

S⁶ = 0

6/2{2a+(6-1)d} =0

3{2a+5d } =0

2a+5d =0.........¹

a⁴ = 2

a+3d = 2 ..........²

form eq2

a= 2-3d

put a in eq1

2(2-3d)+5d =0

4-6d +5d =0

-d = -4

d= 4

put d =4 in a

a = 2-3(4) = 2-12 = -10

now

we have to find S³⁰

S³⁰ = 30/2{ 2 × -10 +(30-1)×4}

= 15{ -20 + 29×4}

= 15 × 96

S ³⁰ = 1440