In an AP the seventh term is 38 and the twelfth term is 63. What is the sum of the first twenty terms?

Answer: 1110

Step-by-step explanation:

For an arithmetic progression, the nth term is gotten by using the formula:

= a + (n-1) d

Therefore,

7th term = a + 6d = 38 ... equation i

12 term = a + 11d = 63 ... equation ii

Subtract equation i from ii

(a + 6d) - (a + 11d) = 38 - 63

-5d = - 25

d = 25/5

d = 5

Since d = 5

From a + 6d = 38

a = 38 - 6d

a = 38 - (6*5)

a = 38 - 30

a = 8

The sum of the first 20 terms will be:

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

= 20/2[ (2*8) + (20-1) 5]

= 10[16 + (19 * 5) ]

= 10 (16+95)

= 10 (111)

= 1110