Question

the sum of the first three terms of an Arithmetic progression A.P. is 42 and the product of the first and the third term is 52. Find the first term and common difference.​

Answer 1

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Answer 2

The first term of the AP is 14 and the common difference is 12 or -12.

• Let the three terms of the AP be a-d , a , a+d.

• The sum of first three terms of the AP is 42.

Therefore,

a -d +a + a + d = 42

3a = 42

a = 14

• Now , product of first and third term of the AP is

(a-d)(a+d) = 52

a² - d² = 52

14² - d² = 52

d² = 196 - 52

d² = 144

d = 12 or d = -12

• The first term of the AP is 14 and the common difference is 12 or -12