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Question Number 174844 by daus last updated on 12/Aug/22

Commented by daus last updated on 12/Aug/22

$$plshelpforD$$$$a^k+a^{k+2}+.....n^{th}term$$

Answered by Rasheed.Sindhi last updated on 12/Aug/22

$$D.$$$$a^k+a^{k+2}+.....n^{th}term$$$$\mathit{a}=a^k,\mathit{r}=a^{k+2}/a^k=a^{k+2-k}=a^2$$$${\mathit{S}}_{\mathit{n}}=\frac{\mathit{a}({\mathit{r}}^{\mathit{n}}-1)}{\mathit{r}-1}=\frac{a^k({\left(a^2\right)}^n-1)}{a^2-1}$$$$=a^k({\left(a^2\right)}^{n-1}+{\left(a^2\right)}^{n-2}+...+a^2+1)$$$$=a^k(a^{2n-2}+a^{2n-4}+...+a^2+1)$$

Commented by daus last updated on 13/Aug/22

$$howtodecidewhichformulatousebecause$$$$idonknowr>1orr<1?$$

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