What is the fifth term of the sequence whose first term is 10 and whose common ratio is 1/2?

Solution:

It is given that, the first term is 10 and whose common ratio is 1/2.

A common ratio of half means that to get each successive term, you have to multiply the preceding term by half.

The general term or the n^th term of a GP is found by using the formula t_n = a.r^n-1

t₅ = 10.½ ^5-1

t₅ = 10/2⁴

= 10/16 = 5/8

Let us verify this:

1^st term = 10

2^nd term = 10 × 1/2 = 5

3^rd term = 5 × 1/2 = 5/2

4^th term = 5/2 × 1/2 = 5/4

5^th term = 5/4 × 1/2 = 5/8

Therefore, the fifth term of the sequence is 5/8.

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What is the fifth term of the sequence whose first term is 10 and whose common ratio is 1/2?

Summary:

The fifth term of the sequence whose first term is 10 and whose common ratio is 1/2 is 5/8.