Find the nth term of the following

Question

-7,-2,3,8

Answer 1

To find the nth term of the sequence $-7,-2,3,8$, let's first analyze the pattern.

1. Identify the differences between consecutive terms:
   • From $-7$ to $-2$: difference = $-2-(-7)=5$
   • From $-2$ to $3$: difference = $3-(-2)=5$
   • From $3$ to $8$: difference = $8-3=5$

All the differences are constant and equal to $5$, which indicates that this sequence is an arithmetic sequence with a common difference of $5$.

2. The formula for the nth term of an arithmetic sequence is:

$$a_n=a_1+(n-1)d$$

Where:

• $a_1$ is the first term of the sequence.
• $d$ is the common difference.
• $n$ is the term number.

3. For this sequence:

• $a_1=-7$
• $d=5$

Plugging in these values:

$$a_n=-7+(n-1)\cdot 5$$

4. Simplifying this expression:

$$a_n=-7+5n-5$$ $$a_n=5n-12$$

So the nth term of the sequence is:

$$\boxed{{\displaystyle 5n-12}}$$