Question

Use the rule t_n=5∙2^(n-1) to find the first five terms in the geometric sequence.

i have no clue what they are talking about by geometric sequence and oll that can i get some help plz thanks.

Answer 1

5, 10, 20, 40, 80.

Explanation:

A geometric sequence is one where each term after the first is found by multiplying the previous term by a constant value.

For example, 2, 6, 18, 54 . Here each term is multiplied by 3 to get the next term. The 3 is called the common ratio.

The explicit formula for the nth term is t_n = a1. r^(n - 1) where a1 = the first term, r = the common ratio.

The first term of your sequence is 5.2^(1-1) = 5*2^0 = 5 and the second term is 5.2^2^(2-1) = 5*2^1 = 5*2 = 10. Note the common ratio (the value that we multiply by) is 2.

So the first 5 terms are 5, 10, 20, 40, 80.