Q. 11

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

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

a10 = 41 and a18 = 73

We know, an = a + (n – 1)d where a is first term or a1 and d is the common difference and n is any natural number

When n = 10:

a10 = a + (10 – 1)d

a10 = a + 9d

Similarly, When n = 18:

a18 = a + (18 – 1)d

a18 = a + 17d

According to question:

a10 = 41 and a18 = 73

a + 9d = 41 ………………(i)

And a + 17d = 73…………..(ii)

Subtracting equation (i) from (ii):

a + 17d – (a + 9d) = 73 – 41

a + 17d – a – 9d = 32

8d = 32

d = 4

Put the value of d in equation (i):

a + 9(4) = 41

a + 36 = 41

a = 41 – 36

a = 5

As, an = a + (n – 1)d

a26 = a + (26 – 1)d

a26 = a + 25d

Now put the value of a = 5 and d = 4 in a26

a26 = 5 + 25(4)

a26 = 5 + 100

a26 = 105

Hence, 26th term of the given A.P. is 105

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses