In an AP, if the common difference $(d) = –4$, and the seventh term $( a_{7})$ is 4, then find the first term.
Given: Common difference $( d)=–4$, and the seventh term $(a_{7})=4$.
To do: To find the first term of the given A.P.
Solution:
Let the the first term of the A.P. is a.
Common difference , $d=-4$
Seventh term, $a_{7}=4$
As known $n^{th}$ term of the A.P. $a_{n}=a+(n-1)d$
By using the formula,
$a_{7}=a+(7-1)(-4)=4$
$\Rightarrow a-24=4$
$\Rightarrow a=24+4$
$\Rightarrow a=28$
Thus the first term of the given A.P. is 28.
 
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