Question

Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4^th terms is ______.

Options

• –1

• – 8

• 7

• – 9

Answer 1

Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4^th terms is 7.

Explanation:

Let the common difference of two APs are d₁ and d₂, respectively.

Bycondition, d₁ = d₂ =d   ......(i)

Let the first term of first AP (a₁) = –1

And the first term of second AP (a₂) = – 8

We know that, the n^th term of an AP, T₁ = a + (n – 1) d

∴4th term of first AP, T₄ = a, + (4 – 1)d = – 1 + 3d.

And 4th term of second AP, T’₄ = a₂ + (4 – 1)d = – 8 + 3d

Now, the difference between their 4th terms is i.e.,
|T4 – T’4|

= (–1 + 3d) – (– 8 + 3d)

= –1 + 3d + 8 – 3d

= 7

Hence, the required difference is 7.