What is the $20$th term of the arithmetic sequence with first term $a_…

Question

What is the $20$th term of the arithmetic sequence with first term $a_{1} = 4$ and common difference $d = -3$?

Accepted Answer

A. $-53$

$a_{n} = a_{1} + (n - 1)d$.
$a_{20} = 4 + (20 - 1)(-3) = 4 + 19 \cdot (-3) = 4 - 57 = -53$.
- Trap B ($-50 = 4 + 18(-3)$) uses $n - 2$.
- Trap C ($-47 = 4 - 51 + ...$) miscomputes $19 \cdot 3$.
- Trap D ($+61$) gets the sign of $d$ wrong.
When $d$ is negative, the sequence *decreases* — by term 20, the sequence has fallen $57$ units below $a_{1}$.

Answer

$-50$

Answer

$61$

Answer

$-47$