Answer
See answer below.
Work Step by Step
The sum of an arithmetic sequence is given by: $S_n=\dfrac{n}{2}[a_1+a_n]$ and the nth term for an arithmetic sequence is given by $a_n=a_1+(n-1) d$
We are given that $a_n=3 \cdot 5^n $
Here, $\dfrac{a_2}{a_1}=\dfrac{3 \cdot 5^2}{3 \cdot 5^1}=5 ; \\\dfrac{a_3}{a_2}=\dfrac{3 \cdot 5^3}{3 \cdot 5^2}=5; \\ \dfrac{a_4}{a_3}=\dfrac{3 \cdot 5^4}{3 \cdot 5^3}=5; \\\dfrac{a_5}{a_4}=\dfrac{3 \cdot 5^5}{3 \cdot 5^4}=5$
It has been noticed that the quotient of every consecutive term is the same or constant.
Hence, the result has been proved.
