Question

What is the next number in the sequence: 9, 16, 24, 33…?

Answer 1

For solving this question you should know about the sequence of numbers. We can calculate the sequence rule by subtracting any term from the next term of that and doing this for 2 - 3 continuous terms and then we will find a fixed pattern of increasing of the terms. And this pattern is known as sequence.

Complete step-by-step answer:
According to our question we have to find the next term of the sequence 9, 16, 24, 33…. As we know that the sequence of any queue is in the pattern of a fixed rule. And every next digit of that sequence will be written by the rule. If we see in our question then the sequence is given as, 9, 16, 24, 33,… If we subtract to two continuous digits, then, we get,
$\begin{aligned} & 16-9=7 \\\ & 24-16=8 \\\ & 33-24=9 \\\ \end{aligned}$
It seems that the second term is 7 greater than the first term and the third term is 8 greater than the second term and the fourth term is 9 greater than the third term and so on. So, it will be fixed that the next term which is the fifth term will be 10 greater than the fourth term. So, it will be $33+10=43$. And if we make the sequence rule then:
$\Rightarrow {{\left( n+1 \right)}^{th}}\text{term}\Rightarrow \left[ \left( {{\left( n+1 \right)}^{th}}\text{term}-{{n}^{th}}\text{term} \right)+1 \right]={{\left( n+2 \right)}^{th}}\text{term}$
And if we check this then:
$\begin{aligned} & {{T}_{1}}=9 \\\ & {{T}_{2}}=16 \\\ & {{T}_{3}}=16+\left( 16-9 \right)+1=\left( 7+1 \right)+16=16+8=24 \\\ & {{T}_{4}}=24+\left( 24-16 \right)+1=24+8+1=33 \\\ & {{T}_{5}}=33+\left( 33-24 \right)+1=33+9+1=43 \\\ \end{aligned}$
So, it is true and the next number is 43.

Note: For calculating the sequence of any continuous terms we always find the sequence rule first and then calculate the next values from that. And every sequence has a fixed rule but we have to find it carefully and first apply it for the given terms and then find the other terms.