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An arithmetic sequence is represented by the function a_n=a_n−1+15, where a_1=10. What is the 12th term of the sequence?

User Werulz
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Final answer:

To find the 12th term of the arithmetic sequence, use the recursive formula an = an-1 + 15 with a1 = 10. Substitute the values to find the 12th term.

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. In this case, the sequence is defined by the formula an = an-1 + 15, where a1 = 10.

To find the 12th term of the sequence, we can use the formula:

a12 = a11 + 15

Substituting the value of a1 and using the recursive formula, we can find the 12th term as follows:

a2 = a1 + 15 = 10 + 15 = 25

a3 = a2 + 15 = 25 + 15 = 40

Continuing this pattern, we find that:

a12 = a11 + 15 = a10 + 15 + 15 = ... = a1 + (12-1) * 15 = 10 + 11 * 15 = 175

Therefore, the 12th term of the arithmetic sequence is 175.

User Maxim Dsouza
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