Class 10 Math All topics Arithmetic Progressions

Find $n$ if the given value of $x$ is the $n_{th}$ term of the AP: $521 ,11,1621 ,22,...$ ; $x=550$.

(a)

$100$

(b)

$110$

(c)

$200$

(d)

$220$

Correct answer: (a)

Solution:

Here, first term $a=521 =211 $ and the common difference $d=11−211 =211 .$

Given, $a_{n}=x=550$

$⇒a+(n−1)d=550$

$⇒211 +(n−1)×211 =550$

$⇒1+(n−1)=550×112 $

$⇒n=100$

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