Question

What is the next number in the sequence $9,16,24,33,...$ ?

Answer 1

Hint: We write the equation in the first line and then write the equation again in the next line but now, starting with a space in the front. We then subtract the second row from the first row and find out that the difference is an AP. We now find the difference corresponding to $33$ , which is $10$ and then add it to $33$ , to get $43$ which will be the next term.

Complete step by step solution:
A sequence is an enumerated collection of objects, especially numbers, in which repetitions are allowed and in which the order of objects matters. A sequence may be finite or infinite depending on the number of objects in the sequence. Sequences can be of various types such as arithmetic sequence, geometric sequence and so on. Sequences can be completely random as well. The ${{n}^{th}}$ term of a sequence is sometimes written as a function of n.
In the given sequence $9,16,24,33,...$ , we can see that the numbers of the sequence are neither in arithmetic nor geometric sequence. So, let us rewrite the same sequence in the next line but with one space gap. In other words, we rewrite the sequence as,
$\begin{align}
& 9,16,24,33,... \\
& 9,16,24,... \\
\end{align}$
We subtract the bottom row from the top row, keeping in mind to subtract only the corresponding elements and get,
$9,7,8,9,...$
Now, if we apply a little intuition, we can see that from the second term onwards, the terms represent the difference in terms. Clearly, the difference is an arithmetic sequence with a common difference $1$ . This means that the next difference will be $9+1=10$ . This means that $10$ should be added to $33$ , to get the next term of the sequence which will be $33+10=43$ .
Thus, we can conclude that the next term of the sequence will be $43$ .

Note: A sequence is an enumerated collection of objects, especially numbers, in which repetitions are allowed and in which the order of objects matters. A sequence may be finite or infinite depending on the number of objects in the sequence. Sequences can be of various types such as arithmetic sequence, geometric sequence and so on. Sequences can be completely random as well. The ${{n}^{th}}$ term of a sequence is sometimes written as a function of n.
In the given sequence $9,16,24,33,...$ , we can see that the numbers of the sequence are neither in arithmetic nor geometric sequence. So, let us rewrite the same sequence in the next line but with one space gap. In other words, we rewrite the sequence as,
$\begin{align}
& 9,16,24,33,... \\
& 9,16,24,... \\
\end{align}$
We subtract the bottom row from the top row, keeping in mind to subtract only the corresponding elements and get,
$9,7,8,9,...$
Now, if we apply a little intuition, we can see that from the second term onwards, the terms represent the difference in terms. Clearly, the difference is an arithmetic sequence with a common difference $1$ . This means that the next difference will be $9+1=10$ . This means that $10$ should be added to $33$ , to get the next term of the sequence which will be $33+10=43$ .
Thus, we can conclude that the next term of the sequence will be $43$ .