Question

What is the formula for the arithmetic sequence if the sum of the same sequence is given by sn= 2n+3n^2 ?

Answer 1

Answer:

Let a= First term, d= common difference and tn= nth term of the AP.

Sum of n terms of this AP is,

Sn’ = (n/2)[2a+(n-1)d] = an+(d/2)n²-(dn/2)

Sn’ =n[a-(d/2)]+(d/2)n² ——(1)

Sum of n terms of given AP is,

Sn = 2n+3n² ——(2)

Comparing coefficients of n and n² from eqn. (1) and eqn. (2),

d/2 = 3 and 2 = a-(d/2)

⇒ d= 6

⇒ a = 2+3 = 5

n th term of given AP is,

tn = a+(n-1)d

tn= 5+(n-1)6 = 5+6n-6 = 6n-1

Ans: tn = 6n-1