Question

In an Ap 19th term is 52 and 38th term is 128,find sum of 56 terms

Answer 1

Hello!

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a + 18d = 52 (equation 1)

a + 37d = 128 (equation 2)

Using (equation 1) and (equation 2)

=> a + 18d = 52
a + 37d = 128
(-) (-) (-)
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-19d = -76
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d = -76/ -19

d = 4

Putting value of d in (equation 1)

=> a + 18(4) = 52

= a + 72 = 52

= a = -20

Now, we will find the sum of 56 terms using the formula written below.

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

= S(56) = 56/ 2 [2(-20) + (56 - 1)4]

= S(56) = 28 [-40 + 55(4)]

= S(56) = 28 [-40 + 220]

= S(56) = 28 x 180

= S(56) = 5040

Therefore, the sum of 56 terms = 5040

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I hope it helped.

Thank You!