Question

In an$AP$, if the common difference $d = - 4$ and the seventh term ${a_7}$ is 4, then find the first term.

Answer 1

Here, we are going to use the formula for the nth term of an AP i.e ${a_n} = a + (n - 1)d$.

Complete step-by-step answer:
Given, the common difference $d = - 4$ and the seventh term ${a_7}$ is 4
We know that ${a_n} = a + (n - 1)d$
$\Rightarrow {a_7} = a + (7 - 1)( - 4)$
$\Rightarrow 4 = a - 24$
$\Rightarrow a = 28$
Hence, the first term in the AP is $a = 28$
Therefore, $a = 28$ is the required solution

Note: One should remember the relation between the first term, common difference and the nth term of an AP. If a sequence has negative common difference represents a decreasing arithmetic progression