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.