<s>[INST] Find sum of $n$ terms of the series $12+14+24+58+164+\cdots$ Find sum of $n$ terms:
$12+14+24+58+164+\cdots$
I have tried my best but could not proceed
 [/INST] You can do this by grouping terms and using the geometric sum formula:
$$2[\{6+(1-1)\}+\{6+(3-2)\}+\{6+(9-3)\}+\{6+(27-4)\}+\dots]$$
$$=2[6n+(1+3+9+27+...)-(1+2+3+4+...)]$$
$$=2\bigg[6n+\frac{3^n-1}{3-1}-\frac{n(n+1)}{2}\bigg]$$
$$=12n+3^n-1-n^2-n$$
$$=11n+3^n-1-n^2$$
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