Question

How do you find an equation that describes the sequence 16, 17, 18, 19 ….and 20 and find the ${{23}^{rd}}$ term?

Answer 1

Hint: If the common difference between consecutive terms is always the same then the series is in arithmetic progression. If the first term of arithmetic progression is a and the common difference is d then the nth term of the series is $a+\left( n-1 \right)d$.

Complete step by step answer:
The given series in the question is 16, 17, 18, 19…and 20
We can see that the common difference between every consecutive term is 1.
If the common difference between every consecutive term is the same we can say the sequence is in arithmetic progression.
Now we can see the given sequence is in arithmetic progression and the common difference is 1, the first term of the sequence is 16.
The nth term of an arithmetic progression is equal to $a+\left( n-1 \right)d$ where a is the first term and d is a common difference.
So nth term of given series will be $16+\left( n-1 \right)\times 1$ further solving we can say nth term is $n+15$
If have to evaluate the ${{23}^{rd}}$ term then we put 23 in the place of n in the above formula
So ${{23}^{rd}}$ term of the sequence= $23+15=38$

Note: Always remember the formula for nth term of arithmetic progression and if we have to calculate the sum of n term of arithmetic progression the formula for sum of n terms is $\dfrac{n}{2}\left( 2a+\left( n-1 \right)d \right)$ where a is the first term and d is the common difference.