Question

In an arithmetic progression 19th term is 52 and 38th term is 128,find sum of first 56 terms.

Answer 1

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Answer 2

Here 19th term is 52
Therefore a + 18d = 52

And 38th term is 128
Therefore a + 37d = 128

Now, a + 37d - a - 18d = 128 - 52
19d = 76
d = 4
a + 18(4) = 52
a= 52 - 72
a = -20

Sum of 56 terms = 56/2 { -40 + 55(4)}
=28(-40 + 220)
=28(180)
=5040