Question

Obtain the sum of the 56 terms of an A. P. whose 19th & 38th terms are 32 &
148 respectively.
thoth will have​

Answer 1

Answer:

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.