Answer
The 33th term: $125$
The sum of the first 20 terms: $700$
Work Step by Step
We are given the sequence:
$-3,1,5,9,....$
Compute the difference between consecutive terms:
$1-(-3)=4$
$5-1=4$
$9-5=4$
Since the difference between consecutive terms is constant, the sequence is arithmetic. Its elements are:
$a_1=-3$
$d=4$
Determine $a_{33}$:
$a_n=a_1+(n-1)d$
$a_{33}=-3+(33-1)(4)$
$a_{33}=125$
Determine the sum of its 20 terms $S_{20}$:
$S_n=\dfrac{n(2a_1+(n-1)d)}{2}$
$n=20$
$S_{20}=\dfrac{20(2(-3)+(20-1)(4))}{2}=\dfrac{20(70)}{2}=700$
