Question

the sum of a certain series is given by Sn=n^2+3n, verify the series is A.P

Answer 1

Answer:The sum of the first n terms of a sequence is given by Sn = n(n+2).

Start with S1 = 1*(1+2) = 1*3 = 3. So the first term is 3.

Next, S2 = 2(2+2) = 2*4 = 8. This the sum of the first two terms. Since the first term is 3, the second term is 8–3 = 5.

Next, S3 = 3(3+2) = 3*5 = 15. This the sum of the first three terms. Since the sum of the first two terms is 8, the third term is 15–8 = 7.

Hence the first three terms are: 3, 5, and 7.

hope you get it

Answer 2

Answer:

S1=4

S2=10

S3=18

S4=28

T1=S1=4

T2=S2-S1=6

T3=S3-S2=8

Therefore the series is 4+6+8+......forms an A. P