# 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 4th terms is ______. - Mathematics

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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 4th terms is ______.

• –1

• – 8

• 7

• – 9

#### Solution

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 4th 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 nth 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.

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.1 | Q 11 | Page 46
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