Question

the 5 th term of an arithemetic sequence is 21 and 9th term is 37 what is its common difference? answer with explaination​

Answer 1

Step-by-step explanation:

5th term of an A.P = 21.

9th term of an A.P = 37.

As we know that,

General term of an A.P.

Tₙ = a + (n - 1)d.

⇒ T₅ = 21.

⇒ a + (5 - 1)d = 21.

⇒ a + 4d = 21 ⇒ (1).

⇒ T₉ = 37.

⇒ a + (9 - 1)d = 37.

⇒ a + 8d = 37 ⇒ (2).

From equation (1) & (2), we get.

⇒ a + 4d = 21.

⇒ a + 8d = 37.

We get,

⇒ - 4d = - 16.

⇒ d = 16/4.

⇒ d = 4.

Put the value of d = 4 in equation (1), we get.

⇒ a + 4d = 21.

⇒ a + 4(4) = 21.

⇒ a + 16 = 21.

⇒ a = 21 - 16.

⇒ a = 5.

First term = a = 5.

Common difference = d = 4.

Answer 2

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