Question

If the sum of first n terms of an A.P is 2m²+3m, then find 3rd term and 11th term. step by step.

Answer 1

We have:
Sn = 3n + n2
We know:
tn = Sn – S(n – 1) 
Thus, we have:
tn = 3n + n2 – 3(n – 1) – (n – 1)2
   = 3n + n2 – 3n + 3 – n2 – 1 + 2n
   = 2n + 2

(i)
To find the first term, we will put n = 1 in tn = 2n + 2.
Thus, we get:
t1 = 2(1) + 2 = 2 + 2 = 4
To find the sum of the first two terms, we will put n = 2 in Sn = 3n + n2.
Thus, we get:
S2 = 3(2) + (2)2 = 6 + 4 = 10

(ii)
To find the second term, we will put n = 2 in tn= 2n + 2.
Thus, we get:
t2 = 2(2) + 2 = 4 + 2 = 6

To find the third term, we will put n = 3 in tn = 2n + 2.
Thus, we get:
t3 = 2(3) + 2 = 6 + 2 = 8

To find the 15th term, we will put n = 15 in tn = 2n + 2.
Thus, we get:
t15 = 2(15) + 2 = 30 + 2 = 32

Answer 2

Answer:

Step-by-step explanation: