In each of the following geometric sequences find an express

In each of the following geometric sequences, find an expression for (i) the 17th term. (ii) for the nth term.

a.) 2,2square3,6...

b.) 2,-2square2...

c.) -square5,5...

Solution

Solution :

a)   We have the geometric sequence 2 , 2^2 , 2^3 , 2^4 , .... That is, 2 , 4 , 8 , 16 , .....

In mathematics, a geometric progression (also inaccurately known as a geometric series) is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.

The n^th term of the geometric sequence is given by   a_n = a₁ * r^n-1

We have first term a₁ = 2 and common ratio r = 4/2 = 2

i ) Now we have to find the 17^th term. So just replace n by 17 into the formula, we get

a₁₇ = a₁ * r^17-1

a₁₇ = 2 * (2)¹⁶

a₁₇ = 131072

ii) Now we have to find the n^th term.

a_n = a₁ * r^n-1

a_n = 2 * (2)^n-1