Math, asked by KingAR7, 1 year ago

In an A.P. of 19th term is 52 and 38th term is 128 find sum of first 56 terms

Answers

Answered by priya1357
5
a19=52
a+18d=52
a=52-18d
a38=128
a+37d=128
52-18d+37d=128
52+19d=128
19d=76
d=4
a=52-18*4
a=52-72
a=-20

a56=a+55d
-20+55*4
-20+220
=200 is the answer
Answered by vyaswanth
5
T19=52

a+(n-1)d=52

a+(19-1)d=52

a+18d=52 -------(1)

T38=128

a+(n-1)d=128

a+(38-1)d=128

a+37d=128 -------(2)

subract equation (2) - (1)

a+37d-(a+18d)=128-52

19d=76

d=4

substitute in equation (1)

a+18d=52

a+18×4=52

a+72=52

a=(-20)

Sn=n/2(2a+(n-1)d)

S56=56/2(-40+(56-1)4)

S56=28×180

S56=5040

sum of 56 terms is 5040
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