The 8th term of an A.P., whose first two terms are - 5 and 2 respectively, is :

Step 1: Identify the first term and common difference

In an Arithmetic Progression (A.P.), the first term is denoted by $a_1$ and the common difference by $d$. We are given the first two terms, $a_1 = -5$ and $a_2 = 2$. The common difference $d$ is found by subtracting any term from its succeeding term.

Step 2: Calculate the common difference

Substitute the given values of the first and second terms into the formula for the common difference. Subtracting $-5$ from $2$ gives $2 + 5$, which simplifies to $7$. So, the common difference is $7$.

Step 3: Apply the formula for the nth term

The formula for the $n$ -th term of an Arithmetic Progression is $a_n = a_1 + (n-1)d$, where $a_n$ is the $n$ -th term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference. We need to find the 8th term, so $n=8$.

Step 4: Calculate the 8th term

Substitute the values $a_1 = -5$, $n = 8$, and $d = 7$ into the formula for the $n$ -th term. First, calculate $(8-1)$, which is $7$. Then multiply $7$ by the common difference $7$ to get $49$. Finally, add this to the first term, $-5$, to find the 8th term.

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