Verified Answer :

\(\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_1=\textit{first term}\\ n=n^{th}\ term\\ r=\textit{common ratio} \end{cases}\)

\(\bf -----------------------------\\ \begin{array}{ccllll} term&value\\ x&y\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 1&5\cdot (1.25)^{1-1}\\ 2&5\cdot (1.25)^{2-1}\\ 3&5\cdot (1.25)^{3-1}\\ 4&5\cdot (1.25)^{4-1}\\ 5&5\cdot (1.25)^{5-1}\\ 6&5\cdot (1.25)^{6-1}\\ \end{array}\)

Answer:Given below

Step-by-step explanation:

Given

a=5

common ratio(r)=1.25

therefore next term is \(ar,ar^2.......\)

\(a_2=ar=5\times 1.25=6.25\)

\(a_3=ar^2=5\times 1.25^2=7.8125\)

\(a_4=ar^3=5\times 1.25^3=9.765\)

\(a_5=ar^4=5\times 1.25^4=12.207\)

\(a_6=ar^5=5\times 1.25^5=15.258\)

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