Question

2. Find an A.P. whose 2nd term is 10 and the 6th term exceeds the 4th term by 12
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Answer 1

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, 16..........

Answer 2

Answer:

Step-by-step explanation:

Given :-

2nd term is 10 and the 6th term exceeds the 4th term by 12.

To Find :-

A.P

Solution ;-

⇒ a + 5d = a + 3d  +12

⇒ 5d - 3d = 12

⇒ 2d = 12

⇒ d = 12/2

⇒ d = 6

⇒ a + d = 10

⇒ a + 6 = 10   [Putting d value]

⇒ a = 10 - 6

⇒ a = 4

Now Finding 6th and 4th term

6th Term

= a + 5d

= 4 + 5(6)

= 4 + 30

= 30

4th Term

= a + 3d

= 4 + 3(6)

= 4 + 18

= 22

Hence, the terms of A.P are 4, 10, 16, 22, 28, 34, .......