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Q: What is the tenth term if the first term is -10 and the common difference is -2?

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It is a + 8d where a is the first term and d is the common difference.

a + 99d where 'a' is the first term of the sequence and 'd' is the common difference.

From any term after the first, subtract the preceding term.

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If the first term, t(1) = a and the common difference is r then t(n) = a + (n-1)*r where n = 1, 2, 3, ...

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It is a + 8d where a is the first term and d is the common difference.

What is the 14th term in the arithmetic sequence in which the first is 100 and the common difference is -4? a14= a + 13d = 100 + 13(-4) = 48

a + 99d where 'a' is the first term of the sequence and 'd' is the common difference.

100 - 13(4) = 48 or 100 + 13(4) = 152. (It was not stated whether the difference given is [term - preceding term] or [term - succeeding term]. * * * * * The common difference is defined as [term - preceding term] so the first answer is the correct one: 100 - 13*4 = 48

From any term after the first, subtract the preceding term.

If the first term is 12 and the seventh term is 36, then we have gone up 36-12 in the space of 6 term changes. This is 24 per 6 changes, which can be written as the division 24/6. This works out as 4. Thus the common difference in the sequence is 4.

The nth term is Un = a + (n-1)*d where a = U1 is the first term, and d is the common difference.

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100 + 13(-4) = 100 - 56 = 48

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