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Question

Find the sums given below:
$$7+10\cfrac{1}{2}+14+......+84$$


Solution

Here, $$a=7$$
$$d=10\dfrac{1}{2}-7=\dfrac{21}{2}-7=\dfrac{7}{2}$$
Also, last term $$l=84$$
$$a_n=l=a+(n+1)d$$
$$84=7+(n-1)\dfrac{7}{2}$$
$$84-7=(n-1)\dfrac{7}{2}$$
$$n-1=77\times\dfrac{2}{7}$$
$$n-1=22$$
$$n=23$$
$$S=\dfrac{n}{2}(a+l)$$
$$S=\dfrac{23}{2}(7+84)$$
$$S=\dfrac{23\times91}{2}$$
$$S=1046.5$$

Mathematics

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