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Q.

If the sum of the series, 54+51+48+. . . . is 513, then find the number of terms.


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a

18

b

20

c

17

d

None of these 

answer is A.

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Detailed Solution

Given, the sum of the series, 54+51+48+. . . . is 513.
Here, a=54 and d=-3.
As we know sum of an AP,
Sn=n2(2a+(n-1)×d)
⇒ 513=n2(2×54+(n-1)×(-3))  ⇒ 513=n2(111-3n)
 ⇒ 111n-3n2=1026 Solving the quadratic equation for n, we get,
n=18 Hence, the correct option is 1.
 
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