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If the 7th term of an AP is twice the third ter... - JAMB Mathematics 2005 Question

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
correct option: b

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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