Question

sum of the first nth term of an arithmetic sequence is 3n2+5n find the first term and common different and write the algebraic from of the sequence​

Answer 1

Answer:

Sum of n terms of an AP is

$\frac{n}{2} (2a + (n - 1)d) = 3 {n}^{2} + 5n \\ \frac{n}{2} (2a + (n - 1)d) = n(3n + 5) \\ 2a + nd - d = 6n + 10 \\ on \: comparing \\ d = 6 \: and \: 2a - d = 10 \\ 2a - 6 = 10 \\ 2a = 16 \\ a = 8$

Algebraic expression is

a + (n - 1)d

= 8 + (n - 1)×6

= 8 + 6n - 6

= 2 + 6n

Answer 2

Answer:

S1 = first term (a) = 8

second term = S2 - S1 = 22 - 8 = 14

common difference (d)

= second term - first term = 6

Sequence is 8, 14, 20, 26.....

nth term = 8 + (n -1) 6 = 6n + 2