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

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

3 0

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

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