Question

If the sum of 'n'terms of an A P is 2n+3n²,generate the progression and find the nth term

Answer 1

$sum \\ = \frac{n}{2} (2a + (n - 1)d) \\ = \frac{2an + d {n}^{2} - dn}{2} \\ = \frac{(2a - d)n + d {n}^{2} }{2} = 2n + 3 {n}^{2} \\ \: comparing \\ d = 6 \\ a = 5 \\ hence \: ap$
5,11,17,23........
$nth \: term \\ = 5 + (n - 1)6 \\ 5 + 6n - 6 \\ 6n - 1$

Answer 2

Given, Sum of n terms of an A. P. = 2n+3n²



Putting value of n=1,

S1 = 2 *1 + 3* 1²

S1 = 2+3 = 5.

S1 = a 1

First term of the A. P. = 5.

For n = 2,

S2 = 2 * 2 + 3 * 2²

S2 = 4 + 12 = 16.

S2 - S1 = a2

a2 = 16 - 5 = 11.

Second term, a 2 = 11.

Common difference, d = a2 - a1 = 11 - 5 = 6.

✔️A.P. = 5, 11, 17, 23, 29......

⏺️nth Term,

an = a + ( n - 1 ) d

an = 5 + ( n - 1 ) 6.

an = 5 + 6n - 6

✔️an = 6n - 1.