If the sum of a certain number of terms of the AP 25, 22, 19, ...… - Vidyadip

Question

If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.

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Answer

Sum of terms 25, 22, 19, ... is 116 $\frac{\text{n}}{2}[50+(\text{n}-1)(-\text{3})]=116$ $\frac{\text{n}}{2}[53-3\text{n}]=116$ $53\text{n}-3\text{n}^2=232$ $3\text{n}^2-53\text{n}+232=0$ $3\text{n}^2-29\text{n}-24\text{n+232=0}$ $\text{n}(3\text{n}-29)-8(3\text{n}-29)=0$ $(3\text{n}-29)(\text{n}-8)=0$ $\Rightarrow\text{n}=8$ or $\frac{29}{3}$ N connor be in fracti on, so $\text{n}=8$ Last term $=25-7\times3=4$

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