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.

Answer 1

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=$\frac{10}{2}[108\times 2+(10-1\left)2\right]=216+81=234\times 5=1170$