Question

The sum of n terms of an arithmetic sequence is 4n²+5n. Then its nth term is _____​

Answer 1

$\text{Sum of arithmetic series,}\\\\S_n = \dfrac{n}{2} \left[2a + (n-1)d \right]\\\\\\\implies 4n^2 +5n = \dfrac{n}2 [2a +(n-1)d] \\\\\\\implies \dfrac{8n^2 + 10 n}n = 2a + (n-1)d \\\\\\\implies a + a + (n-1)d = \dfrac{n(8n+10)}n \\\\\\\implies a + (n-1)d = 8n+10 -a = \text{nth term}$