The sum of the first three terms of an Arithmetic Progression (A:P.) i

1.	The sum of the first three terms of an Arithmetic Progression (A:P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Answer» Let the first three terms of an A.P. be a – d, a and a + d. According to the statement, we have a – d + a + a + d = 42 3a = 42 a = 14 Now,(a – d)(a + d) = 52 a² – d² = 52 14² – d² = 52 ⇒ d² = 196 – 52 = 144 ⇒ d = ± 12 Hence, the first term is 14 and common difference is ± 12.

The sum of the first three terms of an Arithmetic Progression (A:P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.

Answer»

Let the first three terms of an A.P. be a – d, a and a + d.

According to the statement, we have

a – d + a + a + d = 42

3a = 42

a = 14

Now,(a – d)(a + d) = 52

a² – d² = 52

14² – d² = 52

⇒ d² = 196 – 52 = 144

⇒ d = ± 12

Hence, the first term is 14 and common difference is ± 12.