Question

In an AP, if the common difference (d) is -4 and the seventh term $\left( {{a_7}} \right)$ is 4, then find the first term.

Answer 1

Hint- Use the concept that any ${n^{th}}$ term of an AP is written as ${a_n} = a + (n - 1)d$

Given that in an A.P the common difference $d = - 4$ and the seventh term ${a_7} = 4$
Let a be the first term of the A.P and ${a_n}$be the ${n^{th}}$term of the A.P such that ${a_n} = a + (n - 1)d$
So the seventh term of the A.P that is ${a_7}$ can be written as
${a_7} = a + (7 - 1)d$
Substituting the values we get
$
  4 = a + (7 - 1)( - 4) \\
   \Rightarrow 4 = a - 24 \\
   \Rightarrow a = 28 \\
 $
Thus the first term of the A.P is $a = 28$

Note- Whenever we face such types of problems the key concept involved is to simplify the general formula of ${n^{th}}$ term of an A.P series. This will help you reach the right answer.