5th term is 7 and 7th term is 5 what is the common differnce and what is the first term of this sequence
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In the AP, a = -8.
The ratio of the 7th and the 9th terms is a+6d : a+8d = 5:8, or
8(a+6d) = 5(a+8d) or
8a + 48d = 5a + 40d, or
48d-40d = 5a-8a
8d = -3a, or
d = -3a/8 = (-3)*(-8)/8 = 3.
The common difference is 3.
And the AP is -8, -5, -2, 1, 4, 7, 10, 13, 16
The 7th term is 10 and the 9th term is 16 and their ratio is 10:16 or 5:8. Correct.
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