Question

The 10^th and 18^th terms of an A.P. are 41 and 73 respectively. Find 26^th term.

Answer 1

In the given problem, we are given 10^th and 18^th term of an A.P.

We need to find the 26^th term

Here

`a_10 = 41`

`a_18 = 73`

Now we will find `a_10` and `a_18` using the formula `a_n = a + (n -1)d`

So,

`a_10 = a + (10 - 1)d`

41 = a + 9d  ....(1)

Also

`a_18 = a + (10 - 1)d`

73 = a + 17d .....(2)

So to solve for a and d

On subtracting (1) from (2) we get

8d = 32

`d - 32/8`

d = 4

Substiting d= 4 in (1) we get

41 = a + 9(4)

41 - 36 = a

a = 5

Thus

a = 5

d = 4

n = 26

Substiting the above values in the formula `a_n = a + (n -1)d`

`a_26 = 5 + (26 - 1)4`

`a_26 = 5 + 100`

`a_26 = 105`

Therefore `a_26 = 105`