Question

Write the value of a₃₀ − a₁₀ for the A.P. 4, 9, 14, 19, ....

 

Answer 1

In this problem, we are given an A.P. and we need to find a₃₀ - a¹⁰.

A.P. is   4,9,14,19 .....

Here,

First term (a) = 4

Common difference of the A.P. (d) = 9 -4  

= 5 

Now, as we know,

a_n = a + (n- 1) d

Here, we find a₃₀ and a₂₀.

So, for 30^th term,

a₃₀ =  a + (30 - 1 ) d

      = 4 + (29)(5)

      = 4 + 145

       = 149

Also, for 10^th term,

a₂₀ = a +(10-1) d

      = 4 + (9 ) (5) 

      = 4 + 45 

      = 49

So,

a₃₀ - a₁₀ = 149 - 49

                = 100

Therefore, for the given A.P a₃₀ - a₁₀ = 100 .