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Question

18 terms are inserted between 3 and 45 such that the resulting sequence is an AP. The sum of the resulting (finite) AP including the terms 3 and 45 is ___.

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Solution

Including the terms 3 and 45, the number of terms in the AP will be 20.
Now in the AP, the first term will be 3 and the last term will be 45 and the sum of n terms is Sn=n2(first term+last term).
The value of first term(a) = 3, last term(l) = 45 and number of terms(n) = 20.
S20=202(3+45)=10(48)=480

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