Question

write a recursive formula for the following arithmetic sequence.\\{-100, -200, -300, -400, \dots\\}\
select one:\
\bigcirc a. $a_n = a_{n-1} + 200$, for $n \geq 2$, $a_1 = -100$.\
\bigcirc b. $a_n = a_{n-1} - 100$, for $n \geq 2$, $a_1 = -100$\
\bigcirc c. $a_n = a_{n-1} - 200$, for $n \geq 2$, $a_1 = -100$.\
\bigcirc d. $a_n = a_{n-1} + 100$, for $n \geq 2$, $a_1 = -100$.

Explanation:

Step1: Identify first term

The first term $a_1$ of the sequence is $-100$.

Step2: Find common difference

Calculate the difference between consecutive terms: $-200 - (-100) = -100$, $-300 - (-200) = -100$. The common difference is $-100$.

Step3: Build recursive formula

For an arithmetic sequence, the recursive formula is $a_n = a_{n-1} + d$ for $n\geq2$, where $d$ is the common difference. Substitute $d=-100$ and $a_1=-100$.

Answer:

B. $a_n = a_{n-1} - 100$, for $n \geq 2$, $a_1 = -100$