Question

the sum of n terms of an ap is 5n2+3n.find ap and its 10th termpls help me to answer this question get 50 points by answering correct question

Answer 1

Hey there,

You can simply calculate sum of 10 terms s₁₀ and subtract sum of 9 terms s₉ to get 10th term a₁₀.

a₁₀=s₁₀-s₉
=[5(10²)-3(10)]-[5(9²)-3(9)]
=470-378
=92

Hence the 10th term is 92.

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Answer 2

$S_n=5n^2+3n$
we know,
$T_n=S_n-S_{n-1} \\ \\ = 5 {n}^{2} + 3n - 5 {(n - 1)}^{2} - 3(n - 1) \\ \\ = 5( {n}^{2} - {n}^{2} + 2n - 1) + 3(n - n + 1) \\ \\ = 5(2n - 1) + 3 \\ \\ = 10n - 2$

$Hence, T_n=10n-2$
now, 10th term = T₁₀ = 10 × 10 - 2 = 98