If the sum of n terms of AP is 2 n2-5 then prove that an is equal to 4 n-3 -

Correction:Given Sₙ = 2n² + 5n S₁ = 2×1 + 5×1 = 7 S₂ = 2×(2²) + 5×2 = 8 + 10 = 18 Therfore First term a₁ = 7 amp; Second term a₂ = 18 7 = 11 and ther ...

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Standard X

Mathematics

General Form of an AP

If the sum of...

Question

If the sum of n terms of AP is 2n²+5 then prove that a_n is equal to 4n+3 ?

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Solution

Correction:Given Sₙ = 2n² + 5n

S₁ = 2×1 + 5×1 = 7

S₂ = 2×(2²) + 5×2 = 8 + 10 = 18

Therfore First term a₁ = 7 & Second term a₂ = 18 - 7 = 11
and therefore common difference 'd' = 11 - 7 = 4

Now nth term
aₙ = a₁ + (n-1)d

= 7 + ( n - 1) 4

aₙ = 7 + 4n - 4

aₙ = 4n + 3
Hence Proved!

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If the sum of n terms of AP is 2n2+5 then prove that an is equal to 4n+3 ?

If the sum of n terms of AP is 2n²+5 then prove that a_n is equal to 4n+3 ?