Question

What is the term of the sequence 8 35 143 ___ 575?
1.195
2.223
3.323
4.313
5.296

Answer 1

Hint: In this problem, we have to find the missing term of the sequence. We can see that the given terms in the sequence are the squared terms of 6 multiples which are then subtracted to 1. We can now say that the missing term will also be a squared term subtracted to 1. We can now find it from the following steps.

Complete step by step answer:
Here we have to find the missing term of the sequence 8 35 143 ___ 575.
We can see that the terms in the sequence are the squared (multiple of 6) and then subtracted to 1, where the first term is,
\[\Rightarrow 8={{\left( 3 \right)}^{2}}-1\]
We can now write the second term,
\[\Rightarrow 35={{\left( 6 \right)}^{2}}-1\]
The third term is the squared term of 3,
\[\Rightarrow 143={{\left( 12 \right)}^{2}}-1\]
The fifth term is the squared term of 4,
\[\Rightarrow 575={{\left( 24 \right)}^{2}}-1\]
We can see that the missing fourth term can be,
\[\Rightarrow {{\left( 18 \right)}^{2}}-1=323\]
Therefore, the missing term of the sequence 8 35 143 ___ 575 is 323.

Note: Students should know that the given sequence in this problem has no common difference, so we cannot use any formulas to find the missing term. For these types of problems, we have to find the missing term by solving logically as here we can see the terms are the squared terms of 6 multiples subtracted to 1.