How do you find a general formula for each arithmetic sequence given 8th term is 20; 17th term is 47?
Subtracting first equation from second, we get
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To find the general formula for an arithmetic sequence, you can use the formula for the (n)th term of an arithmetic sequence:
[ a_n = a_1 + (n  1) \times d ]
Where:
 ( a_n ) is the (n)th term of the sequence.
 ( a_1 ) is the first term of the sequence.
 ( d ) is the common difference between consecutive terms.
 ( n ) is the term number.
Given: The 8th term (( a_8 )) is 20. The 17th term (( a_{17} )) is 47.

Using the formula for the 8th term: [ a_8 = a_1 + 7d = 20 ] [ a_1 + 7d = 20 ] ... (i)

Using the formula for the 17th term: [ a_{17} = a_1 + 16d = 47 ] [ a_1 + 16d = 47 ] ... (ii)
To find ( a_1 ) and ( d ), solve the system of equations (i) and (ii).
Subtracting (i) from (ii) to eliminate ( a_1 ): [ 16d  7d = 47 + 20 ] [ 9d = 27 ] [ d = 3 ]
Substituting ( d = 3 ) into (i) to find ( a_1 ): [ a_1 + 7(3) = 20 ] [ a_1  21 = 20 ] [ a_1 = 1 ]
The general formula for the arithmetic sequence is: [ a_n = 1 + (n  1)(3) ] [ a_n = 1  3n + 3 ] [ a_n = 4  3n ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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