If the nth term of a progression is (4n – 10) show that it is an AP.

1.	If the nth term of a progression is (4n – 10) show that it is an AP. Find its(i) first term,(ii) common difference, and(iii) 16th term.
Answer» n^th term of AP is 4n – 10 (Given) Putting n = 1, 2, 3, 4, …, we get At n = 1: 4n – 10 = 4 x 1 – 10 = 4 – 10 = -6 At n = 2: 4n – 10 = 4 x 2 – 10 = 8 – 10 = -2 At n = 3: 4n – 10 = 4 x 3 – 10 = 12 – 10 = 2 At n = 1: 4n – 10 = 4 x 4 – 10 = 16 – 10 = 6 We see that -6, -2, 2, 6,… are in AP (i) first term = -6 (ii) Common difference = -2 – (-6) = 4 (iii) 16th term: Using formula: a_n = a + (n – 1)d Here n = 16 a₁₆ = -6 + (16 – 1)4 = 54

If the nth term of a progression is (4n – 10) show that it is an AP. Find its(i) first term,(ii) common difference, and(iii) 16th term.

Answer»

n^th term of AP is 4n – 10 (Given)

Putting n = 1, 2, 3, 4, …, we get

At n = 1: 4n – 10 = 4 x 1 – 10 = 4 – 10 = -6

At n = 2: 4n – 10 = 4 x 2 – 10 = 8 – 10 = -2

At n = 3: 4n – 10 = 4 x 3 – 10 = 12 – 10 = 2

At n = 1: 4n – 10 = 4 x 4 – 10 = 16 – 10 = 6

We see that -6, -2, 2, 6,… are in AP

(i) first term = -6

(ii) Common difference = -2 – (-6) = 4

(iii) 16th term:

Using formula: a_n = a + (n – 1)d

Here n = 16

a₁₆ = -6 + (16 – 1)4 = 54