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# If the sum of certain number of terms of the A.P., $25,22,19................$ is $116$, then find the last term.

$\begin{array}{1 1} 7 \\ 1 \\ 4 \\ -2 \end{array}$

Toolbox:
• Sum of $n$ terms of an $A.P.=S_n=\large\frac{n}{2}$$[(2a+(n-1)d] • n^{th}\:term=t_n=a+(n-1)d Given that sum of n terms of the A.P. is 116 i.e.,\:\:S_n= 25+22+19+........+t_n=116 In this A.P. first term a=25, common difference d=22-25=-3 We know that S_n=\large\frac{n}{2}$$[(2a+(n-1)d]$