QUESTION

# An arithmetic progression 5, 12, 19,… has 50 terms. Find out the last term.

Hint:
Form the first 3 terms find out the common difference of the arithmetic progression. The first term and the common difference are known to us. Therefore, we can find out the last term or the 50th term by using the formula:
${{a}_{n}}=a+\left( n-1 \right)d$, where a is the first term, d is the common difference and ${{a}_{n}}$ is the ${{n}^{th}}$ term of the arithmetic progression.

Complete step-by-step solution:
We know that arithmetic progression is a sequence of numbers in order that the difference of any two successive numbers is a constant value. The difference between any two successive terms is known as the common difference.
Here the series is given as 5, 12, 19,…
Therefore the first term of the series is 5. The common difference is:
12 – 5 =7 or 19 – 12 = 7.
We know that is a is the first term of the arithmetic progression series and d is the common difference then the ${{n}^{th}}$ term of the series will be:
${{a}_{n}}=a+\left( n-1 \right)d$
In this problem, a = 5, d = 7, n = 50.
Therefore,
${{a}_{50}}=5+\left( 50-1 \right)\times 7=5+\left( 49\times 7 \right)=5+343=348$
Hence, the last term of the given series is 348.

Note:
Alternatively we can find out the last term by adding the common difference with the previous term. Like, after 19 the next number will be 19 + 7 = 26, then 26 + 7 = 33. But, in the given problem this process will be very lengthy as we need to find out the 50th term. It is better to use the formula here.