Give the sequence 7,14,21,......84 . Find the number of term

Question

ScanSolve AI Tutor · Accepted Answer

Okay Duke, let's find the number of terms in this sequence.

The given sequence is $7, 14, 21, \dots, 84$ .

Identify the type of sequence.
Check the difference between consecutive terms:
$14 - 7 = 7$
$21 - 14 = 7$
Since the difference is constant, this is an Arithmetic Progression (AP).
Identify the first term ( $a$ ), the common difference ( $d$ ), and the last term ( $a_n$ ).
The first term, $a = 7$ .
The common difference, $d = 7$ .
The last term, $a_n = 84$ .
Use the formula for the $n$ -th term of an AP.
The formula for the $n$ -th term of an AP is $a_n = a + (n-1)d$ .
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.
$12$

Answer