Answer:
Given,
10th term of an A.P is 41, and 18th terms of an A.P. is 73
a10 = 41
a18 = 73
an = 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
an = 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
26th term of the given A.P. is 105.