Find the number of terms in the arithmetic sequence 7, 10, 13, ..., 55.

Question

ScanSolve AI Tutor · Accepted Answer

To find the number of terms in the arithmetic sequence, we use the formula for the $n^{th}$ term of an arithmetic sequence.

Given the sequence: $7, 10, 13, ..., 55$

Identify the first term ( $a_1$ ).
The first term is $a_1 = 7$ .
Calculate the common difference ( $d$ ).
The common difference is the difference between consecutive terms:
$d = 10 - 7 = 3$
$d = 13 - 10 = 3$
So, the common difference is $d = 3$ .
Identify the last term ( $a_n$ ).
The last term given in the sequence is $a_n = 55$ .
Use the formula for the $n^{th}$ term of an arithmetic sequence.
The formula is:
$a_n = a_1 + (n-1)d$
Substitute the known values into the formula:
$55 = 7 + (n-1)3$
Solve the equation for $n$ .
First, subtract 7 from both sides:
$55 - 7 = (n-1)3$ $48 = (n-1)3$
Next, divide both sides by 3:
$\frac{48}{3} = n-1$ $16 = n-1$
Finally, add 1 to both sides to find $n$ :
$n = 16 + 1$ $n = 17$
The number of terms in the sequence is $\text{17}$ .

Answer