Question

Two given A.P.'s are 2,7,12, and 18,21,24, If nth term of both the progressions are equal then find the value of n.​

Answer 1

Step-by-step explanation:

nth term of both the progressions are equal. Hence, n = 16. Hence, the value of n and nth term is 16 and –21, respectively.

Answer 2

First A.P → 2, 7, 12

Here

• First term = a = 2
• Common difference = d = 5

Second A.P → 18, 21, 24

Here

• First term = a = 18
• Common difference = d = 3

According to the question

aₙ of First A.P = aₙ of Second A.P

a + (n - 1)d = a + (n - 1)d

⇒ 2 + (n - 1)5 = 18 + (n - 1)3

⇒ 2 + 5n - 5 = 18 + 3n - 3

⇒ 5n - 3 = 3n + 15

⇒ 5n - 3n = 15 + 3

⇒ 2n = 18

⇒ n = 18 ÷ 2

∴ n = 9

So, the value of n = 9

KNOW MORE:

Set of Terms are said to be in A.P when there is a constant difference between the numbers