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arithmetic sequence

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Find the sum of an arithmetic series

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Q. arithmetic sequence

Arithmetic Sequence Formula: To find the number of terms in an arithmetic sequence, we can use the formula for the $n$ th term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n$ th term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms.
Identify First Term: First, we identify the first term $a_1$ of the sequence, which is $3$ .
Find Common Difference: Next, we identify the common difference $d$ of the sequence. The difference between consecutive terms is $7 - 3 = 4$ .
Given Last Term: We are given the last term of the sequence $a_n$ , which is $99$ .
Set Up Equation: Now we can set up the equation $99 = 3 + (n - 1)4$ to solve for $n$ .
Simplify Equation: Simplify the equation: $99 = 3 + 4n - 4$ .
Combine Like Terms: Combine like terms: $99 = 4n - 1$ .
Isolate Term with $n$ : Add $1$ to both sides to isolate the term with $n$ : $99 + 1 = 4n$ .
Solve for n: Simplify the equation: $100 = 4n$ .
Calculate Value of n: Divide both sides by $4$ to solve for n: $100 \div 4 = n$ .
Calculate Value of n: Divide both sides by $4$ to solve for n: $100 \div 4 = n$ .Calculate the value of n: $25 = n$ .

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