Question

Given a term in a geometric sequence and the common ratio, find the explicit formula, a11=5120 ans r=-2

Answer 1

Answer:

$U_n=5(-2)^{n-1}$

Step-by-step explanation:

Given a geometric sequence, the nth term of the geometric sequence is obtained by using the formula:

$U_n=ar^{n-1}$

If the eleventh term, $a_{11}=5120$

and the common ratio, r=-2.

Then:

$5120=a(-2)^{11-1}\\a=\frac{5120}{2^{10}} =5$

The explicit formula for the sequence is:

$U_n=5(-2)^{n-1}$