Exercise 9 Page 334

Explicit equations for geometric sequences follow a specific format. a_n= a_1* r^(n-1) In this form, a_1 is the first term in a given sequence, r is the common ratio from one term to the next, and a_n is the {\color{#FF0000}{n}}^\text{th} term in the sequence. For this exercise, the first term is a_1= 13. Let's observe the other terms to determine the common ratio r. 13* 2 ⟶26* 2 ⟶52* 2 ⟶104... By substituting a_1= 13 and r= 2 into the explicit equation and simplifying, we can find the formula for this sequence.

a_n=a_1* r^(n-1)

SubstituteII

r= 2, a_1= 13

a_n= 13* 2^(n-1)

This equation can be used to find any term in the given sequence. To find a_7, the {\color{#FF0000}{7}}^\text{th} term in the sequence, we substitute 7 for n.

a_n=13 * 2^(n-1)

Substitute

n= 7

a_7=13 * 2^(7-1)

SubTerm

Subtract term

a_7=13 * 2^6

CalcPow

Calculate power

a_7 = 13 * 64

Multiply

Multiply

a_7 = 832

The 7^\text{th} term in the sequence is 832.