The 10th and 18th term of an A.P. are 41 and 73 respectively, find 26th term.

Answer:

Given,

10^th term of an A.P is 41, and 18^th terms of an A.P. is 73

a₁₀ = 41

a₁₈ = 73

a_n = a + (n – 1) d

When n = 10,

a₁₀ = a + (10 – 1)d

= a + 9d

When n = 18,

a₁₈ = a + (18 – 1)d

= a + 17d

 

a₁₀ = 41 and a₁₈ = 73

a + 9d = 41 ………………(i)

And a + 17d = 73…………..(ii)

Subtract equation (i) from (ii),

a + 17d – (a + 9d) = 73 – 41

a + 17d – a – 9d = 32

8d = 32

d = 32/8

d = 4

Put the value of d in equation (i) ,

a + 9(4) = 41

a + 36 = 41

a = 41 – 36

a = 5

a_n = a + (n – 1)d

a₂₆ = a + (26 – 1)d

= a + 25d

Put the value of a = 5 and d = 4 in a₂₆

a₂₆ = 5 + 25(4)

= 5 + 100

= 105

26^th term of the given A.P. is 105.