Which of the following is the term of the arithmetic progression -7, -12, -17, -22…… will be -82 and -107 term of the AP?

# Which of the following is the term of the arithmetic progression -7, -12, -17, -22…… will be -82 and -107 term of the AP?

1. A
n = 16 and n = 21
2. B
3. C
4. D

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### Solution:

Given AP : -7,-12,-17,-22,….., -82,…..
${A}_{n}=A+\left(n-1\right)d$
$⇒-107=-7+\left(n-1\right)\left(-5\right)$
$⇒\frac{-100}{-5}=n-1$
$⇒n=21$
-82 is 16th Term of AP and -107 is 21 Term of AP.
Hence, Option (1) is the correct answer.

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