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 a. 1 b. -7 c. 7 d. 9
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 a. 1 b. -7 c. 7 d. 9
Solution
The fourth term of an arithmetic progression (AP) is given by the formula a + 3d, where a is the first term and d is the common difference.
For the first AP, the first term (a1) is 1. So, the fourth term (T4) is 1 + 3d.
For the second AP, the first term (a2) is -8. So, the fourth term (T4) is -8 + 3d.
The difference between the fourth terms of the two APs is (1 + 3d) - (-8 + 3d) = 1 + 8 = 9.
So, the answer is d. 9.
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