What is the 83rd term of the arithmetic sequence left-brace a subscript n baseline right-brace equals left-brace negative 22 comma negative 18 comma negative 14 comma ellipsis right-brace?

Question

(1 point)
Responses

negative 350
Image with alt text: negative 350

302
302

306
306

354

Answer 1

To find the 83rd term of the arithmetic sequence given by \( a_n \), we first need to determine the first term \( a_1 \) and the common difference \( d \).

From the sequence:

• The first term \( a_1 = -22 \)
• The second term is \( -18 \)

To find the common difference \( d \): \[ d = a_2 - a_1 = -18 - (-22) = -18 + 22 = 4 \]

Now, we can use the formula for the \( n \)-th term of an arithmetic sequence: \[ a_n = a_1 + (n - 1)d \]

Substituting the values we have:

• \( a_1 = -22 \)
• \( d = 4 \)
• \( n = 83 \)

Now, calculate \( a_{83} \): \[ a_{83} = -22 + (83 - 1) \cdot 4 \] \[ = -22 + 82 \cdot 4 \] \[ = -22 + 328 \] \[ = 306 \]

Thus, the 83rd term of the arithmetic sequence is \( \boxed{306} \).