Question

given that the sum of the first n term of a series is sn=2n^2 + 3n . show that it is an arithmetic sequence. state its first term and common difference.​

Answer 1

To show that the given series is an arithmetic sequence, we need to demonstrate that the difference between consecutive terms is constant. The first term is 5 and the common difference is 9.

Step-by-step explanation:

To show that the given series is an arithmetic sequence, we need to demonstrate that the difference between consecutive terms is constant. Let's start by finding the difference between the first two terms:

d = s2 - s1

= (2(2)^2 + 3(2)) - (2(1)^2 + 3(1))

= (8 + 6) - (2 + 3)

= 14 - 5

= 9

Since d is a constant value of 9, we can conclude that the series is an arithmetic sequence. The first term (a1) is given by s1 = 2(1)^2 + 3(1) = 2 + 3 = 5, and the common difference (d) is 9.