The 7th term of an AP is -1 and its 16th term is 17. Then the nth term of the AP is [[1]].

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 2 N − 15.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The 7th term of an AP is -1 and its 16th term is 17. Then the nth term of the AP is

2 n − 15

.
Given that the 7th term of an AP is

− 1

and its 16th term is 17.
Let a be the first term and d be the common difference of the AP.
Formula used for nth term of A.P.:

t n = a + n − 1 d

t 7 = a + 7 − 1 × d ⇒ − 1 = a + 6 d ⇒ a + 6 d = − 1...... 1

Similarly,

t 16 = a + 16 − 1 × d ⇒ 17 = a + 15 d ⇒ a + 15 d = 17...... 2

Subtracting equation (1) from (2),

9 d = 18 ⇒ d = 189 ⇒ d = 2

Put

d = 2

in equation (1),

a + 6 × 2 = − 1 ⇒ a = − 1 − 12 ⇒ a = − 13

Determining the nth term of the AP,

t n = a + n − 1 d

⇒ t n = − 13 + n − 1 2 ⇒ t n = − 13 + 2 n − 2 ⇒ t n = − 15 + 2 n

Therefore, the nth term of the AP is

2 n − 15

Watch 3-min video & get full concept clarity