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find the 100th term of a certain arithmetic sequence, given that the 7th term is 16 and the 61st term is 232 .

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Final answer:

To find the 100th term of an arithmetic sequence, you need to find the common difference and then use the formula an = a + (n-1)d. In this case, the 100th term is 3404.

Step-by-step explanation:

To find the 100th term of an arithmetic sequence, we need to find the common difference first.

Given that the 7th term is 16 and the 61st term is 232, we can set up two equations:

a + 6d = 16

a + 60d = 232

Solving these equations, we find that a = -200 and d = 36.

Now, we can use the formula for the nth term of an arithmetic sequence:

an = a + (n-1)d

Plugging in the values, we get:

a100 = -200 + (100-1)36 = -200 + 99*36 = 3404

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