the sum of n terms of a sequence is 3n2+4n find the nth term and show that sequence is an - Maths - Arithmetic Progressions

Question

the sum of n terms of a sequence is 3n2+4n find the
nth term and show that sequence is an A p

Lalit Mehra · Accepted Answer

Given, sum of n terms of the A P , $S_{n} = {3 n}^{2} + 4 n$ $n^{t h} t e r m o f t h e g i v e n A P, a_{n} = S_{n} - S_{n - 1}$ $S_{n} = 3 n^{2} + 4 n$ Replacing n by (n â€“ 1) in $S_{n}$ , we get $S_{n - 1} = 3 {(n - 1)}^{2} + 4 (n - 1) = 3 (n^{2} - 2 n + 1) + 4 (n - 1) = 3 n^{2} - 6 n + 3 + 4 n - 4 = 3 n^{2} - 2 n - 1$ $a_{n} = S_{n} - S_{n - 1} ∴ a_{n} = (3 n^{2} + 4 n) - (3 n^{2} - 2 n - 1) \Rightarrow a_{n} = 3 n^{2} + 4 n - 3 n^{2} + 2 n + 1 \Rightarrow a_{n} = 6 n + 1$ Thus, the nth term of the A P is 6n + 1 A sequence is an A P if its nth term is a linear expression in n The nth term of the given sequence is a linear expression in n, so the sequence is an A P

the sum of n terms of a sequence is 3n2+4n.find the nth term and show that sequence is an A.p

the sum of n terms of a sequence is 3n²+4n.find the nth term and show that sequence is an A.p