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 Answer: Option B
Explanation
U_{7} = a + (7 – 1)d
= a + 6d
U_{3} = a + (3 – 1)d
= a + 2d
But U_{7} = 2(U_{3})
∴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