Question

Which of the terms of the A.P. $ 11,22,33,........ $ is $ 550 $ ?
(A) $ 20 $
(B) $ 30 $
(C) $ 40 $
(D) $ 50 $

Answer 1

Hint:
For answering this question we should be aware of the basic concept related to arithmetic progression. The $ {{n}^{th}} $ term of an arithmetic progression is given as $ {{a}_{n}}=a+\left( n-1 \right)d $ where $ a $ is the first term of the arithmetic progression and $ d $ is the common difference of the given arithmetic progression.

Complete step by step answer:
Now considering the question the given arithmetic progression is $ 11,22,....... $
We need to find the term of this arithmetic progression having value $ 550 $.
From the basic concept related to arithmetic progression we know that the $ {{n}^{th}} $ term of an arithmetic progression is given as $ {{a}_{n}}=a+\left( n-1 \right)d $ where $ a $ is the first term of the arithmetic progression and $ d $ is the common difference of the given arithmetic progression.
Let us assume that the $ {{n}^{th}} $ term is $ 550 $ and we know that the first term is $ 11 $ and we can say that the common difference is $ 22-11=11 $ .
Now by substituting these terms we will have
  $ \begin{align}
  & 550=11+\left( n-1 \right)\times 11 \\
 & \Rightarrow 550=11n \\
 & \Rightarrow n=\frac{550}{11} \\
 & \Rightarrow n=50 \\
\end{align} $
Therefore, we can conclude that the $ {{50}^{th}} $ term of the given arithmetic progression is $ 550 $ .
Hence we will mark option D as correct.

Note:
While answering questions of this type we should be aware of basic concepts related to progressions we have different types of progressions like arithmetic, geometric and harmonic. The $ {{n}^{th}} $ term of an arithmetic progression is given as $ {{a}_{n}}=a+\left( n-1 \right)d $ where $ a $ is the first term of the arithmetic progression and $ d $ is the common difference of the given arithmetic progression. The $ {{n}^{th}} $ term of a geometric progression is given as $ {{a}_{n}}=a{{r}^{n-1}} $ where $ a $ is the first term of the geometric progression and $ r $ is the common ratio of the given geometric progression. The harmonic progression is defined as $ \dfrac{1}{{{a}_{1}}},\dfrac{1}{{{a}_{2}}},........... $ where $ \dfrac{1}{{{a}_{1}}} $ is the first term and $ {{a}_{1}},{{a}_{2}},....... $ is the arithmetic progression here so we can say that $ \dfrac{1}{{{a}_{n}}}=\dfrac{1}{{{a}_{1}}+\left( n-1 \right)d} $ where $ d={{a}_{1}}-{{a}_{2}} $ .