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Question

Find the $$60^{th}$$ term of the AP 8, 10, 12, ., if it has a total of 60 terms and hence find the sum of its last 10 terms.


Solution

A.P is 8,10,12......................
Then first term is 8 and common difference is 2.
$$a_{n}=a+(n-1)d$$.
Then $$a_{60}=8+(60-1)2=8+59\times 2=126$$
Last 10 term =$$a_{51},a_{52}..................a_{60}$$
Then $$a_{51}=8+(51-1)2=108$$
So total of last 10 terms=$$\frac{10}{2}\left [ 108\times 2+(10-1)2 \right ]=216+81=234\times 5=1170$$

Mathematics

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