Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $$\mathbf { a } _ { \mathbf { n } }$$ to find $$a _ { 20 }$$ , the 20th term of the sequence.
-Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $190 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.
A) $a _ { n } = 2810 + 190 n ; \$ 5090$
B) $a _ { n } = 3000 + 190 n ; \$ 5280$
C) $a _ { n } = 2810 + 190 ( n - 1 ) ; \$ 4900$
D) $a _ { n } = 3000 + 190 n ; \$ 5090$

Question

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $$\mathbf { a } _ { \mathbf { n } }$$ to find $$a _ { 20 }$$ , the 20th term of the sequence.
-Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $190 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year. 
A) $a _ { n } = 2810 + 190 n ; \$ 5090$
B) $a _ { n } = 3000 + 190 n ; \$ 5280$
C) $a _ { n } = 2810 + 190 ( n - 1 ) ; \$ 4900$
D) $a _ { n } = 3000 + 190 n ; \$ 5090$

Quizplus · Accepted Answer

The general term for an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. Here, $a_1 = 3000$ and $d = 190$, so the formula should be $a_n = 3000 + 190(n - 1)$. However, none of the options exactly match this correct formula, suggesting a misunderstanding in the question's interpretation. The closest option, considering the structure of the sequence and the error in the provided options, is A, assuming a misinterpretation in the sequence's starting point or the calculation method. However, based on the standard formula and given information, none of the options accurately reflect the correct formula or the 20th term calculation.

Write a Formula for the General Term (The Nth Term) an\mathbf { a } _ { \mathbf { n } }an​

Write a Formula for the General Term (The Nth Term) $\mathbf { a } _ { \mathbf { n } }$