2005
Mathematics
67ca00ce0c643c71d77dee1f
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: 3
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
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 = 3THIS WEEK's
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