MATHEMATICS

JAMB 2005 - Question 19

Mathematics 2005 JAMB Past Questions - Question 19: if the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference

if the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference
A:
B:
C:
D:
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Correct Answer

B

Explanation

Let's denote the first term of the arithmetic progression (AP) as 'a' and the common difference as 'd'.We are given that the 7th term of the AP is twice the third term. Mathematically, this can be expressed as:a + 6d = 2(a + 2d)Simplifying this equation, we get:a + 6d = 2a + 4dRearranging the terms, we have:6d - 4d = 2a - a2d = aNow, we are also given that the sum of the first four terms of the AP is 42. The sum of an arithmetic progression can be calculated using the formula:Sum = (n/2)(2a + (n-1)d)For the first four terms, n = 4. Substituting the given values, we have:42 = (4/2)(2a + (4-1)d)42 = 2(2a + 3d)21 = 2a + 3dNow, we can substitute the value of 'a' from the earlier equation (2d = a) into this equation:21 = 2(2d) + 3d21 = 4d + 3d21 = 7dDividing both sides by 7, we find:d = 3Therefore, the common difference of the arithmetic progression is 3.