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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 (A) –1 (B) – 8 (C) 7 (D) –9

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

(A) –1

(B) – 8

(C) 7

(D) –9

Answers (1)

\text{Let the first AP be } a_{1}, a_{2}, a_{3}, \ldots \ldots \ldots \ldots \text{ (1)} \\ \text{Let the second AP be } b_{1}, b_{2}, b_{3}, \ldots \ldots \ldots \ldots \text{ (2)} \\ \text{Given that } a_{1} = -1, \quad b_{1} = -8 \\ \text{Difference between their 4th terms is} \\ a_{4} - b_{4} = (a_{1} + 3d) - (b_{1} + 3d) \\ \text{Given that the common difference of both APs is equal} \\ a_{4} - b_{4} = -1 - (-8) \\ = -1 + 8 \\ = 7 \\

 Hence option (C) is correct

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infoexpert21

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