Question

Find an
a.p. whose 2nd term is 10 and the 6th term exceeds the 4th term by 12

Answer 1

A. P. =4,10,16,22,........

Answer 2

$\huge\sf{\underline{\underline{Solution:}}}$

Given:

• ⇒ a₂ = 10

• ⇒ a₆ = a₄ + 12

To find:

• ⇒ A.P

Formula used:

⇒ an = a + (n - 1)d

Now,

⇒ a₂ = 10

⇒ a + d = 10

⇒ a = 10 - d     ......(1)

Now, according to question,

⇒ a₆ = a₄ + 12

⇒ a + 5d = a + 3d + 12     ......(2)

Now, put the value of 'a' from Eq (1) in Eq (2). We get,

⇒ 10 - d + 5d = 10 - d + 3d + 12

⇒ 10 + 4d = 22 + 2d

⇒ 10 + 4d - 22 - 2d = 0

⇒ -12 + 2d

⇒ 2d = 12

⇒ d = 12/2

⇒ d = 6

Now, put the value of d in Equation (1), we get

⇒ a = 10 - d

⇒ a = 10 - 6

⇒ a = 4

Hence, A.P is 4, 10 , 22 , 28 , 34