Given the sequence of 7, 14, 21 ........84 find the number of them

Question

ScanSolve AI Tutor · Accepted Answer

The given sequence is an arithmetic progression.

Identify the first term, common difference, and the last term.
The first term is $a = 7$ .
The common difference is $d = 14 - 7 = 7$ .
The last term is $l = 84$ .
Use the formula for the $n$ -th term of an arithmetic progression.
The formula is $l = a + (n-1)d$ , where $n$ is the number of terms.
Substitute the values into the formula and solve for $n$ .
$84 = 7 + (n-1)7$
Subtract 7 from both sides:
$84 - 7 = (n-1)7$ $77 = (n-1)7$
Divide both sides by 7:
$\frac{77}{7} = n-1$ $11 = n-1$
Add 1 to both sides:
$n = 11 + 1$ $n = 12$
The number of terms in the sequence is 12.

The number of terms is 12.

Answer