Question

Sum of the terms of an ap is 3n2+6n. Find its nth term

Answer 1

→ $\mathsf{a_n = S_n - S_{n-1}}$

→ $\mathsf{a_n = 3n^2+6n - 3(n - 1)^2 - 6(n - 1)}$

→ $\mathsf{a_n = 3n^2 + 6n - 3(n^2 + 1 - 2n) - 6n + 6}$

→ $\mathsf{a_n = 3n^2 + 6n - 3n^2 - 3 + 6n - 6n + 6}$

→ $\mathsf{a_n = 6n + 3}$

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• Formula used is mentioned first.
• Replace n by n - 1 in equation 3n² + 6n.
• The final value of $\mathsf{a_n}$ is nth term.
• The sum of two terms will remain in substraction.

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nth term is 6n + 3

Answer 2

$\huge \underline \mathfrak {Solution:-}$

Sum of n terms = $\mathsf{3n^2 + 6n}$

Sum of (n-1) terms = $\mathsf{3(n-1)^2 + 6(n-1)}$

By subtracting sum of (n-1) th terms from the sum of nth terms , we can find out the nth term.

nth term of A.P. = Sum of n terms - Sum of (n-1) terms

= $\mathsf{3n^2 + 6n}$-$\mathsf{3(n-1)^2 + 6(n-1)}$

= $\mathsf{3n^2 + 6n - 3(n^2+1-2n) -6(n-1)}$

= $\mathsf{3n^2 + 6n - 3n^2 - 3+6n -6n + 6}$

= $\mathsf{ 6n + 3}$