Question

obtain the sum of fitst 56 term of an A.P whose 19th term & 38 th term are 52 & 148 resp.​

Answer 1

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t19 = 52, t38 = 148

tn = a + (n – 1) d

∴ t19 = a + (19 – 1) d

∴ 52 = a + 18d

∴ a + 18d= 52 ......(i)

t38 = a + (38 – 1) d

∴ 148 = a + 37d

∴ a + 37d= 148 ......(ii)

Adding eq. (i) and (ii)

a + 18d + a + 37d = 52 + 148

∴ 2a + 55d = 200 ....... eq.(iii)

Sn = n/2[2a + (n – 1)d]

∴ S56 = 56/2[2a + (56 – 1) d]

∴ S56 = 28 [2a + 55d]

∴ S56 = 28 [200] [From Eq. (iii)]

∴ S56 = 5600

∴ Sum of first 56 terms of A.P. is 5600.

Answer 2

Answer:

t19=52

t38=148

S56=?

a+18d-a-37d=52-148

-19d=-96

d=96/19

a+18(96/19)=52

find a.

and then put the value of a and d in the formula where n=56

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