# Math

The first term of an A.P is -8. The ratio of the 7th term to the 9th term is 5:8. Calculate the common difference of the progression

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1. Where a=-8
(a+6d)/(a+8d)=5/8

(6d-8)/(8d-8)=5/8

It boils down too

8(3d-4)=5(4d-4)

2(3d-4)=5(d-1)

6d-8=5d-1

d=-1+8=7

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2. Correction on the last part
R.H.S

5(d-1)=5d-5

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3. 8 - 5 is 3 ie 3 is the common difference

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4. a = - 8
Ratio of the 7th and 9th term is a + 6d : a + 8d = 5:8
8(a+6d) = 5(a+8d)
8a+48d=5a+40d
48d - 40d = 5a + 8a
8d = -3a
d = -3a÷8
d = -3×(-8)÷8 = 3
Therefore common difference = 3

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5. Science

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6. Amazing lesson keep it up

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