Question

If t12=-13 and the sum of first 4terms is 24 find the sum of first 10 terms

Answer 1

Given :--

t₁₂ = - 13.
a + 11d  = -13
Multiplying this equⁿ by 2
2a + 22d = -26...............1

S₄ = 4/2 ( 2a + 3d )
S₄ = 2 ( 2a + 3d )
∴ 4a + 6d = 24
∴ 2 ( 2a + 3d ) = 24
∴ 2a + 3d = 12...............2

Now, we have got two equations
By solving them with elimination method

2a + 22d = -26
2a + 3d   = 12
(-) (-)          (-)
___________
       19d = -38
∴ d = -2
and substituting d = -2 in equation 2 we get

2a + 3 * ( -2 ) = 12
2a - 6 = 12
2a = 18
a = 9

∴ a = 9 & d = -2

Now,

S₁₀ = 10/2 ( 2 * 9 + [ 10 - 1 ] * -2 )
S₁₀ = 5 * ( 18 + [ - 18 ] )
S₁₀ = 5 * 0
S₁₀ = 0.

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Hope this helps you...