Question
Find the general term of an arithmetic sequence where the twelfth term is 22 and the common difference is d=-6
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Answer to a math question Find the general term of an arithmetic sequence where the twelfth term is 22 and the common difference is d=-6
Tiffany
4.5103 Answers
To find the general term of an arithmetic sequence, we can use the formula:
nth term = a + (n - 1) * d
Where:
- nth term is the term we want to find,
- a is the first term of the sequence,
- n is the position of the term we want,
- d is the common difference between consecutive terms.
In this case, we know that the twelfth term is 22 and the common difference is d = -6.
Let's substitute these values into the formula and solve for the first term a:
12th term = a + (12 - 1) * (-6) = 22
Simplifying the equation:
a - 66 = 22
a = 22 + 66 = 88
Now we have found the first term a = 88.
Therefore, the general term of the arithmetic sequence with a twelfth term of 22 and a common difference of -6 is:
nth term = 88 + (n - 1) * (-6)
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