Question

What are the next three terms in this sequence : 10, 9, 7,4 ?

Answer 1

Hint: To find the next terms we will first observe the pattern of the series. We will try subtracting the second term from the first term, third term from the second term and so on. If we get the same pattern in the numbers then by using the same concept we will get the desired answer.

Complete step by step solution:
We have been given a sequence of numbers 10, 9, 7, 4.
We have to find the next three terms in the given sequence,
Now, let us try to find the pattern of the given sequence. When we subtract the terms, we subtract the second term from the first term, third term from the second term and so on. Then we will get
$\begin{align}
& \Rightarrow 10-9=1 \\
&\Rightarrow 9-7=2 \\
&\Rightarrow 7-4=3 \\
\end{align}$
Now, when we subtract the terms we will get a pattern of numbers such as 1, 2, 3..
So the difference between the next term and 4 will be 4.
So let us assume that the next term will be x. Then we will get
$\begin{align}
&\Rightarrow 4-x=4 \\
& \Rightarrow x=4-4 \\
& \Rightarrow x=0 \\
\end{align}$
Now, the difference between the next term and 0 will be 5.
So let us assume that the next term will be y. Then we will get
$\begin{align}
&\Rightarrow 0-y=5 \\
&\Rightarrow y=0-5 \\
&\Rightarrow y=-5 \\
\end{align}$
Now, the difference between the next term and $-5$ will be 6.
So let us assume that the next term will be z. Then we will get
$\begin{align}
& \Rightarrow -5-z=6 \\
& \Rightarrow z=-5-6 \\
& \Rightarrow z=-11 \\

\end{align}$
Hence we get the next three terms of the sequence as $0,-5,-11$.

Note: The point to be noted is that if the common difference between the terms is the same then the given sequence will be an arithmetic sequence. If the common ratio between the terms is the same then the sequence is a geometric sequence. So in both cases we will find the next terms by using the suitable formulas.