Which term of the sequence for is 607?

Question

Homi · Accepted Answer

Understand the Question

We are given the general formula for the $n^{\text{th}}$ term of a sequence: $t_n = 5n - 3$ for $n \ge 1$ .
To find which term equals $607$ , we set $t_n = 607$ and solve the linear equation for $n$ .
The value of $n$ must be a positive integer representing the position of the term in the sequence.

Step 1 · Solve for $n$

Given $t_n = 5n - 3$ and $t_n = 607$ Diagram 1

\begin{aligned} 5n - 3 &= 607 \\[0.6em] 5n &= 607 + 3 \\[0.6em] 5n &= 610 \\[0.6em] n &= \dfrac{610}{5} \\[0.6em] n &= 122 \end{aligned}

Since $n = 122$ is a positive integer, $607$ is the $122^{\text{nd}}$ term of the sequence.

Answer

$122^{\text{nd}}$ term

Common Mistakes

Transposition Sign Error: Subtracting $3$ from $607$ instead of adding it ( $607 - 3 = 604$ ), which is not divisible by $5$ and leads to an incorrect fractional result.
Non-Integer Check: The term number $n$ must be a natural number ( $n \in \mathbb{N}$ ). If $n$ does not turn out to be an integer, the given number is not a term of the sequence.

Question 4