Question

Which term of the sequence 4, 9, 14, 19, ... is 124 ?

Answer 1

Hint: Note that the given sequence is an arithmetic progression. Identify the first term. Then calculate the common difference. Then use the general formula for the nth term of the A.P. ${{a}_{n}}={{a}_{1}}+\left( n-1 \right)d$. From this equation, find the value of n which is our final answer.

Complete step-by-step answer:

In this question, we are given a sequence 4, 9, 14, 19, ... and that 124 is a part of this sequence.
We need to find the position of 124 in this sequence.
On seeing the given sequence, we will observe that the difference between the consecutive terms is constant. This means that the given sequence is an arithmetic progression, A.P.
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
In the given A.P., the first number is a1 = 4.
Now, let us find the common difference of the A.P.
The common difference is the difference between two consecutive terms.
Let the common difference be d.
So, d = 9 – 4 = 14 – 9 = 5
So, our common difference is 5.
Hence, for our A.P., we have a1 = 4 and d = 5.
Now, we know the general formula for the nth term of the A.P. is
${{a}_{n}}={{a}_{1}}+\left( n-1 \right)d$
We have an = 124, a1 = 4, and d = 5.
Substituting these values in the above equation, we will get the following:
$124=4+\left( n-1 \right)5$
$120=\left( n-1 \right)5$
$\dfrac{120}{5}=\left( n-1 \right) $
$24=\left( n-1 \right)$
$n=25$
Hence, 124 is the 25th term of the given sequence.

Note: In this question, it is very important to identify that the given sequence is an arithmetic progression. You need to know the general formulae and concepts related to Arithmetic Progressions to solve this kind of question. You can see from the series that the odd terms end in 4. You can use this fact to solve the question quickly.