MATHEMATICS

JAMB 2002 - Question 19

Mathematics 2002 JAMB Past Questions - Question 19: If the 9th term of an AP is five times the 5th term,find the relationship between a and d.

If the 9th term of an AP is five times the 5th term,find the relationship between a and d.
A:
B:
C:
D:
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Correct Answer

C

Explanation

Let's assume that the first term of the arithmetic progression (AP) is 'a' and the common difference is 'd'.The formula for the nth term of an AP is given by:Tn = a + (n - 1)dGiven that the 9th term (T9) is five times the 5th term (T5), we can write the following equation:T9 = 5 * T5Substituting the formulas for T9 and T5:a + (9 - 1)d = 5 * (a + (5 - 1)d)Simplifying the equation:a + 8d = 5a + 4dRearranging the terms:8d - 4d = 5a - a4d = 4aDividing both sides by 4:d = aTherefore, the relationship between 'a' and 'd' is that they are equal.

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