The 4th term of an ap is three times the first term and the 7th term exceeds twice the 3rd term by 1.Find the 1st term and the common difference
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Step-by-step explanation:
3a = a + 3d, or
2a = 3d, or
a = (3/2)d …(1)
The 7th term exceeds twice the third term by 1. The relation is
a+6d = 2(a+2d)+1, or
a + 6d = 2a+4d+1, or
2a-a = 6d-4d-1, or
a = 2d-1 …(2). Equate (1) and (2)
a = (3/2)d = 2d-1, or
3d = 4d-2, or
4d-3d=2, or d = 2 and a = 3.
The first term is 3 and the common difference is 3.
Check: The series of the AP is 3,5,7,9,11,13,15.
The 4th term is 9, which is three times the first term.
The 7th term is 15, which is twice the third term plus 1.
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