Question

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

Answer 1

Given that in an A.P., the common difference $d=4$ and the seventh term $a_7=4$.

Let $a_1$ be the first term and $a_n$ be the $nth$ term of the A.P.

Clearly then $a_n=a_1+(n-1)d$

$\Rightarrow a_7=a_1+6d$

$\Rightarrow 4=a_1-24$

$\Rightarrow a_1=4+24=28$.

Thus, the first term is $28$.