Question

Which term of the A.P - 53, -47, -41, is the first positive term.

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Answer 1

We can easily calculate the common difference(d) and first term(a) of the given A.P. We will find the n^{th} term of the A.P and apply a condition that it is greater than zero.

$a=-53$
$d=-47-(-53)$
$=6$

Let $t_n$ be the first positive number
$t_n>0$
$\Rightarrow a+(n-1)d>0$
$\Rightarrow -53+(n-1)d>0$
$\Rightarrow (n-1)X6>53$
$\Rightarrow (n-1)>\frac{53}{6}$
$\Rightarrow n>1+\frac{53}{6}$
$\Rightarrow n>\frac{59}{6}$

Since n is an integer, and $n>\frac{59}{6}$
$n\ge 10$
$\Rightarrow$ The least value is 10
So, ${10}^{th}$ term is the first positive term. You can verify this by finding the $9^{th}$ term and ${10}^{t}h$ term of the A.P. $9^{th}$ term will be negative and ${10}^{th}$ term will be positive