Question

Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is

Options

• 87

• 88

•  89

• 90

Answer 1

In the given problem, we are given 7^th and 13^th term of an A.P.

We need to find the 26^th term

Here,

a₇ = 34

a₁₃ = 64

Now, we will find a₇  and  a₁₃  using the formula 

a_n = a + (n-1) d  

So,

a₇ = a + (7 - 1 ) d 

34 = a + 6d                            .............(1) 

Also,

`a_13 = a + (13 - 1 ) d`

64 = a + 12 d                   ........(2)

Further, to solve for a and d

On subtracting (1) from (2), we get

 64 - 34 = (a + 12d) - (a + 6d)

         30 = a + 12d - a -6d

          30 = 6d

          `d = 30/6`

            d = 5               ................(3) 

Substituting (3) in (1), we get

34 = a + 6(5) 

34 = a + 30 

  a = 34 - 30 

  a = 4

Thus,

a = 4 

d = 5

So, for 18^th term (n = 18),

Substituting the above values in the formula,  a_n = a + (n-1) d

a₁₈ = 4 + (18 - 1) 5

       = 4 + 17 (5) 

       = 4 + 85

       = 89

Therefore, a₁₈ = 89