Question

A geometric sequence starts 5, 15, . . . . Explain how you would calculate the value of the 50th term.

Answer 1

The 50th term of geometric sequence is $5(3)^{49}$

Solution:

Given that, geometric sequence starts 5, 15, . . . .

To find: 50th term

Given is a geometric sequence

Let us find the common ratio between terms

The common ratio is the ratio of a term to the previous term

$r = \frac{15}{5} = 3$

The formula for nth term of geometric sequence is given by:

$a_n = ar^{n-1}$

Where,

$a_n$ is the nth term of sequence

a is the first term of sequence

r is the common ratio

In the given sequence,

first term = a = 5

r = 3

Substituting the values we get,

$a_n = 5(3)^{n-1}$

To find the 50th term, substitute n = 50

$a_{50} = 5(3)^{50-1}\\\\a_{50} = 5(3)^{49}$

Thus the 50th term is found