Question

Find first term, common difference and 5^th term of those sequence which have following n^th term :

(i) 3n + 7

(ii) a + (n – 1)d

(iii) 5 – 3n.

Answer 1

(i) 3n + 7

n^th term, T_n = 3n + 7

First term T₁ = 3 × 1 + 7 = 3 + 7=10

Second term T₂ = 3 × 2 + 7 = 6 + 7=13

Common difference

d = T₂ – T₁

= 13-10 = 3

Fifth term T₅ = 3 × 5 + 7 = 15 + 7 = 22

Hence, a = 10, d = 3 and T₅ = 22

(ii) a+ (n – 1)d

n^th term T_n – a + (n – 1)d

First term T₁ = a + (1 – 1)d

= a + 0 × d = a + 0 = a

Second term T₂ – a + (2 – 1)d = a + d

T₂ = 5 – 3 × 2 = 5 – 6 = -1

Common difference

d = T₂ – T₁= a + d – a = d

Fifth term T₅ = a + (5 – 1)d = a + 4d

Hence, ‘a’ = a,’d’ = d and T₅ = a + 4d

(iii) 5 – 3n

n^th term T_n =5 – 3n

First term, T₁ = 5 – 3 × 1 =5 – 3 = 2

Second term T₂ = 5-3 × 2 = 5- 6 = -1

Common difference

d = T₂ – T₁ = (- 1) -2 = -3

Fifth term T₅= 5 – 3 × 5 = 5 – 15 = – 10

Hence, a = 2, d = -3 and T₅ = – 10