Question

For an AP, if sn=3n²-4n.then an=6n-7​

Answer 1

Answer:

Arithmetic Progressions. If Sn, the sum of first n terms of an A . P. is given by Sn = 3n2 – 4n, then find its nth term. Hence, required nth term is 6n – 7. hope it helps :)

Answer 2

Answer:

If sn=3n²-4n. then an=6n-7​ $\mathrm{n}^{\text {th }} \text { term }=6 \mathrm{n}-7$

Step-by-step explanation:

If Sn, the sum of first n terms of an A . P. is given by Sn = 3n2 – 4n, then find its nth term. Hence, required nth term is 6n – 7. The sum of the third and the seventh terms of an AP is 6 and their product is 8.

Given Sum of n terms is $S_n=3 n^2-4 n$

So Sum of n−1 terms is $\mathrm{S}_{\mathrm{n}-1}=3(\mathrm{n}-1)^2-4(\mathrm{n}-1)$

$\begin{aligned}& =3 n^2-6 n+3-4 n+4 \\& =3 n^2-10 n+7\end{aligned}$

Sum of n terms is equal to sum of n−1 terms plus nth term

$\begin{aligned}& \Rightarrow \mathrm{n}^{\text {th }} \text { term }=\mathrm{S}_{\mathrm{n}}-\mathrm{S}_{\mathrm{n}-1}=3 \mathrm{n}^2-4 \mathrm{n}-\left(3 \mathrm{n}^2-10 \mathrm{n}+7\right) \\& \mathrm{n}^{\text {th }} \text { term }=6 \mathrm{n}-7\end{aligned}$

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