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Ksivusya [100]
4 years ago
8

The first term of an arithmetic sequence is 23 and the 37th term of the sequence is -49. What is the common difference of the se

quence
Mathematics
1 answer:
Leona [35]4 years ago
3 0

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4 years ago
The first term of an AP is -7 and the ratio of the eight term to the third term is 7:1 calculate the common difference
alukav5142 [94]

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the common difference is 6.

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first term of an AP, a = -7

let the common difference = d

The third term is written as;

T₃ = a + 2d

The eight term is written as;

T₈ = a + 7d

The ratio of the eight term to third term = 7:1

\frac{T_8}{T_3} = \frac{7}{1} = \frac{a+ 7d}{a + 2d} \\\\7 =  \frac{a+ 7d}{a + 2d}\\\\Recall, a = -7\\\\7 =   \frac{-7+ 7d}{-7 + 2d}\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = \frac{42}{7} \\\\d = 6

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