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Question

What is the sum of first 14 terms of the H.P. 12,15,18,21....?

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Solution

We know the formula for sum of nth term in arithmetic progression.
The reciprocal of arithmetic progression is harmonic progression.
First term of the given arithmetic series =12
Second term of the given arithmetic series =15
Third term of the given arithmetic series =18
Fourth term of the given arithmetic series =21
Now, Second term - First term =1512=3
Third term - Second term =1815=3
Therefore, common difference of the given arithmetic series is 3.
The number of terms of the given A. P. series (n)=14
We know that the sum of first n terms of the Arithmetic Progress, whose first term =a and common difference =d is
Sn=n2[2a+(n1)d]
S14=142[2×12+(141)3]
S14=7[24+39]
S14=441
Sum of HP =1441

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