If the 7th term of an AP is twice the third term and the sum...

Mathematics

JAMB 2005

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. 6
B. 3
C. 2
D. 1

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Correct Answer: Option B

Explanation

U₇ = a + (7 - 1)d
= a + 6d
U₃ = a + (3 - 1)d
= a + 2d
But U₇ = 2(U₃)
∴a + 6d = 2(a + 2d)
a + 6d = 2a + 4d
2a - a + 4d - 6d = 0
a - 2d = 0 → eqn1
Sn = ⁿ/₂ (2a + (n - 1)d)
42 = ⁴/₂ (2a + (4 - 1)d)
42 = 2(2a + 3d)
21 = 2a + 3d → eqn2
eqn1 * eqn2 0 = 2a - 4d
21 = 7d
∴d = ²¹/₇
d = 3

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