Question

Determine AP Whose 3rd Term Is 11 And The 7th Term Is 29.​

Answer 1

Step-by-step explanation:

Solution :-

Let a be the 1st term and d be the common difference of the AP.

We have,

a₃ = 16

a + 2d = 16 ..... (i)

a₇ = a + 6d and a₅ = a + 4d

According to the questions,

⇒ a₇ - a₅ = 12

⇒ a + 6d - (a + 4d) = 12

⇒ a + 6d - a - 4d = 12

⇒ 2d = 12

⇒ d = 12/2

⇒ d = 6

Putting the value of d in equation (i), we get

a + 2 × 6 = 16

a + 12 = 16

a = 16 - 12 = 4

Here, a = 4, d = 6

Hence, AP is a, a + d, a + 2d, a + 3d +..

4, 4 + 6, 4 + 12, 4 + 18, ...

4, 10, 16, 22..