Question

if the sum of first 6 term of an ap 117 and that of 12 term is 486 find the sum of first 30 terms​

Answer 1

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refer attachment...

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Answer 2

Dear Student,

◆ Answer -

S30 = 3105

● Explanation -

# Given -

s6 = 117

s12 = 486

# Solution -

We know that,

Sn = n/2 [2a + (n-1)d]

S6 = 6/2 (2a + 5d)

117 = 3 (2a + 5d)

2a + 5d = 39 ...(1)

And,

S12 = 12/2 (2a + 11d)

486 = 6 (2a + 11d)

2a + 11d = 81 ...(2)

Eqn (2) - Eqn (1),

(2a + 11d) - (2a + 5d) = 81 - 39

6d = 42

d = 7

So now,

2a + 5d = 39

2a + 5×7 = 39

2a + 35 = 39

2a = 39 - 35

a = 4 / 2

a = 2

Sum of 30 terms is -

Sn = n/2 [2a + (n-1)d]

S30 = 30/2 [2×2 + (30-1)7]

S30 = 15 (4 + 29×7)

S30 = 3105

Hence, the sum of first 30 terms is 3105.

Thanks dear. Hope this helps you...