Question

An arithmetic sequence has first term P0=12 and common difference d=3.

a.) the number 309 is which term of the arithmetic
sequence?

Answer 1

The number 309 is the 100th term of the arithmetic sequence.

Step-by-step explanation:

To find which term of the arithmetic sequence the number 309 is, we need to use the formula:

Sn = P0 + (n - 1)d

where:

• Sn is the nth term of the sequence
• P0 is the first term
• d is the common difference

Plugging in the given values, we have:

Sn = 12 + (n - 1)3

To solve for n, we set Sn equal to 309:

309 = 12 + (n - 1)3

Simplifying the equation:

297 = 3n - 3

3n = 300

n = 100

Therefore, the number 309 is the 100th term of the arithmetic sequence.