Question

True or False? If False, give a reason.

If we know the first and second terms of an arithmetic sequence, then we can find any other term.

Short answer

The given statement is true.

Step-by-step solution

Step 1. Given information.

The given statement is:

If we know the first and second terms of an arithmetic sequence, then we can find any other term.

Step 2. Write the concept.

The $n\text{th}$ term of an arithmetic sequence is:

$a_n=a+\left(n-1\right)d$

Where $a$ is the first term and $d$ is a common difference.

Step 3. Check the given statement.

Let $a_1$and $a_2$are the first two terms of an arithmetic sequence, then

$d=a_2-a_1$

The n^th term of an arithmetic sequence is:

$a_n=a_1+\left(n-1\right)\left(a_2-a_1\right)$

It means, if we know the first and second terms of an arithmetic sequence, then we can find any other term.

Thus, the given statement is true.