Check wheather 101 is term of ap 12,15, 18

1.	Check wheather 101 is term of ap 12,15, 18
Answer» Solution - We have, A.P = 12, 15, 18, ... ⠀ Here, FIRST TERM (a) = 12 Common difference (d) = 3 ⠀ Now, we have to check whether 101 is a term of the GIVEN A.P. or not. For this, we let aₙ = 101 ⠀ We know that, ⠀ ⠀⠀⠀⠀★ aₙ = a + (n - 1)d ⠀ ➝ aₙ = 101 ➝ a + (n - 1)d = 101 ➝ 12 + (n - 1) × 3 = 101 ➝ (n - 1)3 = 101 - 12 ➝ (n - 1)3 = 99 ➝ n - 1 = 99/3 ➝ n - 1 = 33 ➝ n = 33 + 1 ➝ n = 34 ⠀ Therefore, 34th term of the given A.P. is 101. Hence, 101 is a term of A.P.

Answer»

Solution -

We have,

A.P = 12, 15, 18, ...

⠀

Here,

FIRST TERM (a) = 12
Common difference (d) = 3

⠀

Now, we have to check whether 101 is a term of the GIVEN A.P. or not. For this, we let

aₙ = 101

⠀

We know that,

⠀ ⠀⠀⠀⠀★ aₙ = a + (n - 1)d

⠀

➝ aₙ = 101

➝ a + (n - 1)d = 101

➝ 12 + (n - 1) × 3 = 101

➝ (n - 1)3 = 101 - 12

➝ (n - 1)3 = 99

➝ n - 1 = 99/3

➝ n - 1 = 33

➝ n = 33 + 1

➝ n = 34

⠀

Therefore, 34th term of the given A.P. is 101.

Hence, 101 is a term of A.P.

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Check wheather 101 is term of ap 12,15, 18​