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The first term of an ap is -8 and the ratio of the 7th term to the 9th term is 5:8
calculate the common difference of the progression

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Answered by GPT 3.5
To find the common difference of an arithmetic progression (AP), we can use the formula:

nth term = first term + (n - 1) * common difference

Let's use this formula to find the 7th and 9th terms of the AP:

7th term = -8 + (7 - 1) * common difference
9th term = -8 + (9 - 1) * common difference

The ratio of the 7th term to the 9th term is given as 5:8:

(7th term) / (9th term) = 5/8

Plugging in the formulas from above and simplifying the ratio equation:

(-8 + 6 * common difference) / (-8 + 8 * common difference) = 5/8

Cross-multiplying:

8 * (-8 + 6 * common difference) = 5 * (-8 + 8 * common difference)

-64 + 48 * common difference = -40 + 40 * common difference

Subtracting 40 * common difference from both sides and adding 64 to both sides:

64 - 40 = 40 * common difference - 48 * common difference

24 = -8 * common difference

Dividing both sides by -8:

total difference = -8/24 = -1/3

Therefore, the common difference of the arithmetic progression is -1/3.

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