Question

Find the 75th term of the arithmetic sequence given by aₙ = 3n + 1.

A) 226
B) 227
C) 228
D) 229

Answer 1

The 75th term of the arithmetic sequence given by aₙ = 3n + 1 is 226, thus the correct option is A.

Step-by-step explanation:

To find the 75th term of the arithmetic sequence
`\( a_n = 3n + 1 \)`, we can use the formula
`\( a_n = a_1 + (n-1)d \)`, where
`\( a_1 \)` is the first term and d is the common difference.

In this case, the first term
`\( a_1 \)` is given by
`\( a_1 = 3 * 1 + 1 = 4 \)`, and the common difference d is 3. Now, plug these values into the formula:

`\[ a_(75) = 4 + (75-1) * 3 \]`

Simplify the expression:

`\[ a_(75) = 4 + 74 * 3 \]`

`\[ a_(75) = 4 + 222 \]`

`\[ a_(75) = 226 \]`

Therefore, the 75th term of the given arithmetic sequence is 226 , which corresponds to Option A.