Question

Two APs have same common difference . The first term of the one of these is -2 and that of the other is 5. What is difference between their twentieth terms.​

Answer 1

Answer:

the difference between their 20th terms = -7

Step-by-step explanation:

Given,

• Two APs have same common difference
• The first term of the one of these is -2 and that of the other is 5

To find,

• the difference between their 20th terms.​

Formula,

 nth term of A.P.

  $\underline{\boxed{\bf t_n=a+(n-1)d}}$

where

a is the first term

d is the common difference

Solution,

  Let "d" be the common difference of both APs

➢ Let a be the first term of first A.P.

The sequence of first A.P :

 a , a+d , a+2d ,...

First term of first AP = -2

  ∴ a = -2

20th term of first AP,

  a₂₀ = a + (20 - 1)d

  a₂₀ = -2 + 19d

➢ Let A be the first term of second A.P.

The sequence of second A.P. :

A , A + d , A + 2d ,....

First term of second AP = 5

   ∴ A = 5

20th term of second A.P,

   A₂₀ = A + (20 - 1)d

   A₂₀ = 5 + 19d

we have to find the difference between their 20th terms,

  = a₂₀ - A₂₀

  = -2 + 19d - (5 + 19d)

  = -2 + 19d - 5 - 19d

  = -2-5

  = -7

∴ The required answer is "-7"