find the fifth term in 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}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 = 5). [ \begin{align*} a_{5}&=a_{1}r^{5 - 1}\ &=5\times(-3)^{4} \end{align*} ]

Step3: Calculate ((-3)^{4})

((-3)^{4}=(-3)\times(-3)\times(-3)\times(-3)=81)

Step4: Calculate (a_{5})

(a_{5}=5\times81 = 405)

Answer:

(405)