Question 52

What is the value of 162 + 172 + 182 + ……. 252?

Solution

Expression : 162 + 172 + 182 + ……. 252

The above series is an A.P. with first term, $$a=162$$, last term, $$l=252$$ and common difference, $$d=10$$

Let number of terms be = $$n$$

=> Last term = $$l=a+(n-1)d$$

=> $$162+(n-1)10=252$$

=> $$(n-1)10=252-162$$

=> $$(n-1)=\frac{90}{10}=9$$

=> $$n=9+1=10$$

Sum of A.P. = $$\frac{n}{2}(a+l)$$

= $$\frac{10}{2}(162+252)$$

= $$5\times414=2070$$

=> Ans - (D)

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