Question

Find:
(i) 10^th term of the A.P. 1, 4, 7, 10, …..

(ii) 18^th term of the A.P. √2, 3√2, 5√2, …

(iii) nth term of the A.P 13, 8, 3, -2, ….

Answer 1

(i) 10^th term of the A.P. 1, 4, 7, 10, …..

Arithmetic Progression (AP) whose common difference is = a_n – a_n-1 where n > 0

Lets consider as, a = a₁ = 1, a₂ = 4 …

Therefore, common difference, d = a₂ – a₁ = 4 – 1 = 3

To find the 10^th term of A.P, firstly find a_n

By using the formula,

a_n = a + (n - 1) d

= 1 + (n - 1) 3

= 1 + 3n – 3

= 3n – 2

When n = 10:

a₁₀ = 3(10) – 2

= 30 – 2

= 28

Thus, 10^th term is 28.

(ii) 18^th term of the A.P. √2, 3√2, 5√2, …

Arithmetic Progression (AP) whose common difference is = a_n – a_n-1 where n > 0

Let us consider as, a = a₁ = √2, a₂ = 3√2 …

Therefore, common difference, d = a₂ – a₁ = 3√2 – √2 = 2√2

To find the 18^th term of A.P, firstly find a_n

By using the formula,

a_n = a + (n - 1) d

= √2 + (n – 1) 2√2

= √2 + 2√2n – 2√2

= 2√2n – √2

When n = 18:

a₁₈ = 2√2(18) – √2

= 36√2 – √2

= 35√2

Thus, 10^th term is 35√2

(iii) nth term of the A.P 13, 8, 3, -2, ….

Arithmetic Progression (AP) whose common difference is = a_n – a_n-1 where n > 0

Lets consider the, a = a₁ = 13, a₂ = 8 …

Therefore, common difference, d = a₂ – a₁ = 8 – 13 = -5

To find the n^th term of A.P, firstly find a_n

By using the formula,

a_n = a + (n-1) d

= 13 + (n-1) (-5)

= 13 – 5n + 5

= 18 – 5n

Thus, n^th term is 18 – 5n