Question

If an = 3n − 1,then the value of Sn will be

Answer 1

Step-by-step explanation:

Given t

n

=3n−1

To find the series, we will plug in numbers in the above expression.

For n = 1, 3n - 1 = 2

n = 2, 3n - 1 = 5

n = 3, 3n - 1 = 8

So, the sequence we get is 2, 5, 8, 11, .....

Answer 2

Given:

an = 3n − 1

To Find:

Sn = ?

Solution:

Since, Sn =  (n/2)(2a+(n-1)d)

But, a = ?, d = ?

we have,

an = 3n − 1 ------------------(i)

putting n=1 in Equation (i)

a1 = 3*1 - 1

a1 = 3-1 = 2 = a

a2 = 3×2 -1

a2 = 6-1 = 5

d = a2 - a1

d = 5 - 2 = 3

Sn = (n/2)(2*2 + (n-1)3)

Sn = (n/2)(4+3(n-1))

So, Sn = (n/2)(4+3(n-1)).