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 ______.

पर्याय

• –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.

By given condition, 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

T_n = a + (n – 1)d

∴ 4^th term of first AP,

T₄ = a₁ + (4 – 1)d = –1 + 3d

And 4^th term of second AP,

T’₄ = a₂ + (4 – 1)d = – 8 + 3d

Now, the difference between their 4^th terms is i.e.,

|T₄ – T’₄|

= (–1 + 3d) – (– 8 + 3d)

= –1 + 3d + 8 – 3d

= 7

Hence, the required difference is 7.