Question

Which of the following is the explicit rule for a geometric sequence by a recursive formula of an =13a⁽ⁿ−¹⁾ for which the 7th term is 7?

A) 13×7 ⁽ⁿ−¹⁾
B) 7×13⁽ⁿ−¹⁾
C) 7×13⁽ⁿ−¹⁾
D) 13×7⁽ⁿ−¹⁾

Answer 1

The explicit rule for the geometric sequence is A) 13 * 7 ⁽ⁿ−¹⁾.

Step-by-step explanation:

The explicit rule for a geometric sequence by a recursive formula of an = 13a⁽ⁿ−¹⁾ for which the 7th term is 7 is option A) 13×7 ⁽ⁿ−¹⁾.

To find the explicit rule, we need to substitute the given information into the formula. Since we know that the 7th term is 7, we have:

a⁽ⁿ−¹⁾ = 7

13a⁽ⁿ−¹⁾ = 7

Simplifying the equation, we get:

a⁽ⁿ−¹⁾ = 7/13

So, the explicit rule is 13×7 ⁽ⁿ−¹⁾.