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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 4th terms is ______.
Options
–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.
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 nth term of an AP
Tn = a + (n – 1)d
∴ 4th term of first AP,
T4 = a1 + (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.
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