Question

Which of the term of the A.P. 11, 22, 33, 44….. is 550?
(a) 20
(b) 30
(c) 40
(d) 50

Answer 1

We know that the general term expression in an A.P. is as follows: ${{T}_{n}}=a+\left( n-1 \right)d$. In this general term, “a” is the first term of an A.P. and “d” is the common difference of an A.P. Now, a common difference is calculated by taking any one of the terms of the A.P. and then subtract this term from its successor term. Now, substitute the value of ${{T}_{n}}$ as 550 in the general term formula and $''a\And d''$ as well then find the value of n by solving this equation. The value of “n” is the answer we are expecting.

Complete step by step answer:
The A.P. given in the above problem is as follows:
11, 22, 33, 44…..
Now, we are asked to find the order of the term 550 in the above A.P. For that, we are going to use the general term of an A.P. which is equal to:
${{T}_{n}}=a+\left( n-1 \right)d$
In the above formula, $''a''$ is the first term and “d” is the common difference.
Now, we are going to find the value of $''a\And d''$ as $''a''$ is the first term so first term of the A.P. is 11 so the value of $a=11$. After that, we are going to find the value of “d” which is calculated by taking any term say 22 and subtracting 22 from the next term 33 we get,
$33-22=11$
After that, substituting the above calculated values of $''a\And d''$ in the general term formula and we get,
${{T}_{n}}=11+\left( n-1 \right)\left( 11 \right)$
Multiplying 11 by (n – 1) in the above equation we get,
$\begin{aligned} & {{T}_{n}}=11+11n-11 \\\ & \Rightarrow {{T}_{n}}=11n \\\ \end{aligned}$
Now, substituting ${{T}_{n}}$ as 550 in the above equation we get,
$550=11n$
Dividing 11 on both the sides we get,
$\begin{aligned} & \dfrac{550}{11}=n \\\ & \Rightarrow n=50 \\\ \end{aligned}$
Hence, 550 is the ${{50}^{th}}$ term of the given A.P.

So, the correct answer is “Option d”.

Note: The mistake that could be possible in the above problem is while calculating the common difference (d) in the above A.P. The mistake could be you let us take any term from the A.P. say 22 and from this term you subtract the successor term which is 33 and then the common difference will be:
$22-33=-11$
So, make sure you won’t make this mistake in the examination.