The 14th term of an ap is twice
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The 14th term of an AP is twice its 9th term. If its 6th term is -8, then find the sum
of its first 20 terms
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Answer:-
Given:-
In an AP;
a₁₄ = 2 * a₉
We know that,
nth term of an AP (aₙ) a + (n - 1)d
⟹ a + (14 - 1)d = 2 * [ a + (9 - 1)d ]
⟹ a + 13d = 2a + 16d
⟹ 13d - 16d = 2a - a
⟹ - 3d = a -- equation(1).
Also given that;
⟹ a₆ = - 8
⟹ a + 5d = - 8
Substitute the value of a from equation (1).
⟹ - 3d + 5d = - 8
⟹ 2d = - 8
⟹ d = - 8/2
⟹ d = - 4
Substitute the value of d in equation (1).
⟹ a = - 3( - 4)
⟹ a = 12
Now,
Sum of first n terms (Sₙ) = n/2 [ 2a + (n - 1)d ]
So,
S₂₀ = 20/2 [ 2(12) + (20 - 1)( - 4) ]
⟹ S₂₀ = 10 [ 24 + 19( - 4) ]
⟹ S₂₀ = 10 (24 - 76)
⟹ S₂₀ = 10(- 52)
⟹ S₂₀ = - 520
∴ The sum of first 20 terms of the given AP is - 520.
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