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Question

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.


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Solution

Find the sum of all the terms of the series.

Second term, a2=14

Third term, a3=18

We need to find the sum of first 51 terms of the given series.

Common difference, d=a3a2=1814=4

a2=a+d14=a+4

a=10= First term

Sum ofn terms;

Sn=n2[2a+(n1)d]S51=512[2×10+(51-1)4]S51=512[20+(50)×4]S51=512×[20+200]S51=51×110S51=5610

Hence, the sum of first51 terms is 5610.


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