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Question

Find the sum:
$$34+32+30+......+10$$


Solution

In the given series $$34+32+30+......+10$$ the first term is $$34$$ and common difference is $$-2$$.
Let us assume there are $$n$$ terms.
Then $$n$$ th term is $$10$$.
Then $$34+(n-1)(-2)=10$$
or, $$-2(n-1)=-24$$
or, $$n=13$$.
Now the sum of the series is 
$$=\dfrac{13}{2}(10+34)$$
$$=286$$.

Mathematics

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