Question

in an arithmetic sequence third term is 34 and sixth term is 67.Find the common difference​

Answer 1

Given:-

• 3rd term is 34
• 6th term is 67

To Find:-

• Common difference

Solution:-

$\tt \blue{ a_3= a+2d=34 \rightarrow\rightarrow \rightarrow\rightarrow(1)} \\\\\\ \tt \red{a_6=a+5d=67\rightarrow\rightarrow \rightarrow\rightarrow(2)}$

Solving equation (1) and (2)

we get

$\tt a= 12 \\\\ \tt d=11$

Here,

$\tt a = first\: term \\\\ \tt d=common\:difference\\\\ \tt a_x = number of terms$

So common difference is 11

Answer 2

Solution :

• 3rd term of an A.P. = 34
• 6th term of an A.P. = 67

★ General terms of an A.P.

⇒ Tₙ = a + (n - 1)d.

⇒ T₃ = 34.

⇒ T₃ = a + (3 - 1)d.

⇒ T₃ = a + 2d.

⇒ a + 2d = 34. ⇒ (1).

⇒ T₆ = 67.

⇒ T₆ = a + (6 - 1)d.

⇒ T₆ = a + 5d.

⇒ a + 5d = 67. ⇒ (2).

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

⇒ a + 2d = 34.

⇒ a + 5d = 67.

We get,

⇒ - 3d = - 33.

⇒ d = 11.

Put the value of d = 11 in equation (1), we get.

⇒ a + 2d = 34.

⇒ a + 2(11) = 34.

⇒ a = 34 - 22.

⇒ a = 12.

First term = a = 12.

Common difference = d = 11