Question

.What is the 33rd term in the sequence $-3,1,5,9,..........$? What is the sum of the first 20 terms?

Short answer

• The 33rd term of the given sequence is 125.
• The sum of first 20 terms of the sequence is 700.

Step-by-step solution

Step 1. Given information

Sequence is:$-3,1,5,9,....$

Step 2. To find 33rd term of the sequence.

Since in the given sequence the difference between consecutive terms is constant.

Hence, The sequence is an arithmetic sequence.

First term of the sequence :$a=-3$

Common difference is :$$\begin{gathered} d=1-(-3) \\ =1+3 \\ =4 \end{gathered}$$

For 33rd term :$n=33$

So, 33rd term is:

$$\begin{gathered} a_{33}=-3+(33-1)\left(4\right) \\ =-3+32\times 4 \\ =-3+128 \\ =125 \end{gathered}$$

Step 3. To find sum of first 20 terms.

$$\begin{gathered} S_{20}=\frac{20}{2}\left\{2\right(-3)+(20-1\left)4\right\} \\ =10(-6+19(4\left)\right) \\ =10(-6+76) \\ =10\times 70 \\ =700 \end{gathered}$$