MCQ
Which term of the $AP \ \{25, 20, 15,....\}$ is the first negative term ?
- A$10^{\text {th }}$
- B$9^{\text {th }}$
- C$8^{\text {th }}$
- ✓$7^{\text {th }}$
✓
Answer
Correct option: D.
$7^{\text {th }}$
The given $AP$ is $\{25, 20, 15, .....\}$
$a = 25$ and $d = 20 - 25 = -5$
$a_n= a + (n - 1)d < 0$
$\Rightarrow 25 + (n - 1)(-5) < 0$
$\Rightarrow 5 - (n - 1) < 0$
$\Rightarrow 5 - n + 1 < 0$
$\Rightarrow 6 < 0$
So, the frist negative term will be the $7^{\text {th }}$ term.
$a = 25$ and $d = 20 - 25 = -5$
$a_n= a + (n - 1)d < 0$
$\Rightarrow 25 + (n - 1)(-5) < 0$
$\Rightarrow 5 - (n - 1) < 0$
$\Rightarrow 5 - n + 1 < 0$
$\Rightarrow 6 < 0$
So, the frist negative term will be the $7^{\text {th }}$ term.
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