Question

Find the 10th term of the sequence defined by the given rule.
f(1)=2,f(n)=f(n-1)+7

Answer 1

The 10th term of the sequence defined by the rule f(1)=2, f(n)=f(n-1)+7 is found using the arithmetic sequence formula to be 65.

Step-by-step explanation:

The question asks us to find the 10th term of the arithmetic sequence defined by f(1)=2 and f(n) = f(n-1) + 7. An arithmetic sequence is one where each term is equal to the previous term plus a constant difference. Here, the difference is 7. To find the 10th term, we can use the formula for the nth term of an arithmetic sequence, which is f(n) = f(1) + (n - 1)×d, where f(1) is the first term and d is the common difference between the terms.

By substituting the given values into this formula:

• f(1) = 2
• d = 7
• n = 10

We get:

f(10) = 2 + (10 - 1)×7

f(10) = 2 + 9×7

f(10) = 2 + 63

f(10) = 65

Therefore, the 10th term, f(10), of the sequence is 65.