The 18th term of an Ap is 25 find its first term if it's common different is 2

Step 1: Recall the formula for the $n$-th term of an Arithmetic Progression (AP). The formula for the $n$-th term ($T_n$) of an AP is given by: $T_n = a + (n-1)d$ where $a$ is the first term, $n$ is the term number, and $d$ is the common difference.

Step 2: Identify the given values from the problem. We are given: • The 18th term ($T_{18}$) is 25. So, $T_n = 25$ and $n = 18$. • The common difference ($d$) is 2. So, $d = 2$. We need to find the first term ($a$).

Step 3: Substitute the given values into the formula. $25 = a + (18-1)2$

Step 4: Simplify and solve for $a$. $25 = a + (17)2$ $25 = a + 34$ Subtract 34 from both sides to find $a$: $a = 25 - 34$ $a = -9$

The first term of the AP is -9.

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