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