Find the arithmetic progression whose third term is 16 and the seventh

1.	Find the arithmetic progression whose third term is 16 and the seventh term exceeds its fifth term by 12.
Answer» Given, in an A.P a₃ = 16 and a₇ = a₅ + 12 We know that a_n = a + (n – 1)d ⇒ a + 2d = 16…… (i) And, a + 6d = a + 4d + 12 2d = 12 ⇒ d = 6 Using d in (i), we have a + 2(6) = 16 a = 16 – 12 = 4 Hence, the A.P is 4, 10, 16, 22, …….

Find the arithmetic progression whose third term is 16 and the seventh term exceeds its fifth term by 12.

Answer»

Given, in an A.P

a₃ = 16 and a₇ = a₅ + 12

We know that a_n = a + (n – 1)d

⇒ a + 2d = 16…… (i)

And,

a + 6d = a + 4d + 12

2d = 12

⇒ d = 6

Using d in (i), we have

a + 2(6) = 16

a = 16 – 12 = 4

Hence, the A.P is 4, 10, 16, 22, …….