The 4th and 10th terms of an AP are 13 and 25 respectively. Find the first term and the common difference of the AP. Also, find its 17th term.

Open in App

Solution

We have;
T₄ = a + (n - 1)d
⇒ a + 3d = 13 ...(1)

T₁₀ = a + (n - 1)d
⇒ a + 9d = 25 ...(2)
On solving (1) and (2), we get:
a = 7 and d = 2

Thus, we have the following:
(i) First term = 7
(ii) Common difference = 2
(iii) T₁₇ = a + (n - 1)d = a + 16d = 7 + 16 ⨯ 2 = 39

Suggest Corrections

Similar questions

Q. The

4 t h

and

10 t h

terms of an

A . P

. are

13

and

25

respectively.

Find its

(i)

first term

(i i)

common difference

(i i i) 17 t h

term.

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, then find the number of terms in the AP and their sum.

Q. The first and last term of an AP are 17 and 350 respectively. If its common difference is 9. find the numbers of terms in the AP.

Q. If the 10th term of an AP is 52 and the 17th term is 20 more than the 13th term, find the AP.

Q. The first term of an

A P

- 7

and the common difference

5

, find its

10 t h

term.

Join BYJU'S Learning Program

The 4th and 10th terms of an AP are 13 and 25 respectively. Find the first term and the common difference of the AP. Also, find its 17th term.

We have; T4 = a + (n - 1)d ⇒ a + 3d = 13 ...(1) ​T10 = a + (n - 1)d ⇒ a + 9d = 25 ...(2) On solving (1) and (2), we get: a = 7 and d = 2 Thus, we have the following: (i) First term = 7 (ii) Common difference = 2 (iii) T17 = a + (n - 1)d = a + 16d = ​7 + 16 ⨯ 2 = 39

We have;
T₄ = a + (n - 1)d
⇒ a + 3d = 13 ...(1)

T₁₀ = a + (n - 1)d
⇒ a + 9d = 25 ...(2)
On solving (1) and (2), we get:
a = 7 and d = 2

Thus, we have the following:
(i) First term = 7
(ii) Common difference = 2
(iii) T₁₇ = a + (n - 1)d = a + 16d = 7 + 16 ⨯ 2 = 39