Question

The first term of a sequence of numbers is $-3$. Each term after the first is obtained by multiplying the preceding term by $-1$ and then subtracting $1$. What is the ${75}^{th}$ term of the sequence?

• A. $-73$
• B. $-3$
• C. $2$
• D. $4$
• E. $73$

Answer 1

The correct option is B $-3$

First term is $-3$.

Second term is $-3\times -1-1=2$.

Third term is $2\times -1-1=-3$.

Fourth term is $-3\times -1-1=2$. the sequence repeats.

So, the odd terms are $-3$ and even terms are $2$.

Therefore the ${75}^{th}$ term is $-3$.