# How to find the 1st term, the common difference, and the nth term of the arithmetic sequence described below? (1) 4th term is 11; 10th term is 29 (2) 8th term is 4; 18th term is -96

1)

2)

terms respectively on A.P series.

Subtracting equation (2) from equation (1) we get,

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There are many ways to resolve. One of them is apply definition of general term of an arithemtic sequence

Lets check if this general term works

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For both arithmetic sequences, you can use the formulas to find the first term, the common difference, and the nth term.

(1) For the arithmetic sequence where the 4th term is 11 and the 10th term is 29:

Given: ( a_4 = 11 ) and ( a_{10} = 29 )

To find the common difference (( d )), subtract the 4th term from the 10th term and divide by the number of terms between them: ( d = \frac{a_{10} - a_4}{10 - 4} = \frac{29 - 11}{10 - 4} = \frac{18}{6} = 3 )

Then, to find the first term (( a_1 )), use the formula for the nth term: ( a_1 = a_4 - 3(4 - 1) = 11 - 3(3) = 11 - 9 = 2 )

The nth term formula is: ( a_n = a_1 + (n - 1)d )

(2) For the arithmetic sequence where the 8th term is 4 and the 18th term is -96:

Given: ( a_8 = 4 ) and ( a_{18} = -96 )

To find the common difference (( d )), subtract the 8th term from the 18th term and divide by the number of terms between them: ( d = \frac{a_{18} - a_8}{18 - 8} = \frac{-96 - 4}{18 - 8} = \frac{-100}{10} = -10 )

Then, to find the first term (( a_1 )), use the formula for the nth term: ( a_1 = a_8 - (-10)(8 - 1) = 4 - (-10)(7) = 4 + 70 = 74 )

The nth term formula is: ( a_n = a_1 + (n - 1)d )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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