Question

If 12th term of an AP is - 13 and the sum of first 4term is 24 what is the sum of first ten terms

Answer 1

Let a and b are first term and d common difference of an A P.

n th term = tn = a+ ( n - 1 ) d

i) given a₁₂ = - 13

a + 11d = -13 ---------(1)

ii) sum of first 4 terms = 24

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Sₙ = n/2 [ 2a + ( n-1 ) d ]

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S₄ = 24

4/2 [ 2a + 3d] = 24

2[2a + 3d ] = 24

2a + 3d = 12 ------------(2 )

Multiply equation ( 1 ) with 2 and subtract from (2)

We get

-19 d = 38

d = -2

Put d value in (1)

a - 22 = -13

a = -13 + 22

a = 9

iii) a = 9 , d = -2 , n =10

S₁₀ = 10/2 [ 2 × 9 + ( 10 - 1 ) ( - 2 ) ]

    = 5 [ 18 - 18 ]

   = 5 × 0

Therefore,

Sum of first 10 terms = S 10 = 0

I hope this will useful to you.