find the sixth term of the geometric sequence, given the first term and the common ratio.\na₁ = 5 and r =…

Explanation:

Step1: Recall the formula for the nth term of a geometric sequence

The formula for the (n)th term of a geometric sequence is (a_{n}=a_{1}\times r^{n - 1}), where (a_{1}) is the first term, (r) is the common ratio, and (n) is the term number.

Step2: Substitute the given values into the formula

Given (a_{1}=5), (r = 3), and (n=6). Substitute into (a_{n}=a_{1}\times r^{n - 1}), we get (a_{6}=5\times3^{6 - 1}).

Step3: Calculate the exponent

(6-1 = 5), so (a_{6}=5\times3^{5}).

Step4: Calculate (3^{5})

(3^{5}=3\times3\times3\times3\times3=243).

Step5: Calculate (a_{6})

(a_{6}=5\times243 = 1215).

Answer:

(1215)