Mathematics

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

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

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