Q. 75.0( 1 Vote )


The sum of the f

Answer :

Given: T 4 = 2

S 6 = T 1 + T 2 + T 3 + T 4 + T 5 + T 6 = 0
Let the sum of first 30 terms be S30

And, the sum of first six terms be S6.

T 4 = 2

⇒ a + (4 – 1)d = 2
⇒ a + 3d = 2 …………..(i)

We know that,

Also,

S 6 = 0

⇒ 2a + 5d = 0 …………..(ii)

(i)× 2,

a + 3d = 2

2a + 6d = 4 …………………..(iii)

(iii) – (ii),

(2a + 6d) – (2a + 5d) = 4 – 0

⇒ 2a + 6d – 2a – 5d = 4

d = 4
Substituting the value of d = 4 in (i),
a + 3 × (4) = 2

⇒ a + 12 = 2
⇒ a = 2 - 12 = - 10

∴ T 30 = a + 29d
= - 10 + 29 × (4)
= – 10 + 116

= 106
∴ Sum to first 30 terms, 

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