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Question

Find the sum of the arithmetic progressions: 3,92,16,152,...... to 25 terms

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Solution

Given A.P is
3,92,16,152....
number of terms of A.P is n=25
first term of this A.P is a1=3
second term of this A.P is a2=92
common difference
d=a2a1=923=32
we know that sum of n term of an A.P is given by
Sn=n2[2a+(n1)d)]
S25=252[2×3+(251)×32]
S25=12.5[6+(24)×32]
S25=12.5[6+36]
S25=12.5[42]
S25=525
hence the sum of 25 terms of given A.P is 525

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