Question

find the sum to 'N' terms of a G. p whose kth term is 5 ^k

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Answer 1

The $k^{th}$ term of the GP,

$\longrightarrow a_k=5^k$

$\longrightarrow ar^{k-1}=5^{k-1+1}$

$\longrightarrow ar^{k-1}=5\cdot5^{k-1}$

From this we can have,

• $a=5$

• $r=5>1$

Then, sum to $n$ terms of the GP,

$\longrightarrow S_n=\dfrac{a(r^n-1)}{r-1}$

$\longrightarrow S_n=\dfrac{5(5^n-1)}{5-1}$

$\longrightarrow\underline{\underline{S_n=\dfrac{5}{4}(5^n-1)}}$