Question

Find the next term of the given series.
3, 15, 35, 63, 99, ?
$(a)$133
$(b)$143
$(c)$153
$(d)$165

Answer 1

Hint: In the above given question we are asked to find the missing term in the given series. First of all check whether a series is showing an increasing or decreasing pattern. Now, check whether the difference between the two consecutive terms of a series is the same or is changing, that is whether the difference is increasing or decreasing. Then, check whether the series is changing slowly or rapidly and here you will understand the pattern.

Complete step-by-step answer-

We have the given series as:
3, 15, 35, 63, 99, ?
Now, we can write each term in the given series in the form
${2^2} - 1 = 3$
${4^2} - 1 = 15$
${6^2} - 1 = 35$
${8^2} - 1 = 63$
${10^2} - 1 = 99$
${12^2} - 1 = 143$
Here, it can be observed that the required series is of the pattern${(2n)^2} - 1$.
In the above given question, the value of n=1,2,3,4,5,6.
Hence, we get the final series as 3, 15, 35, 63, 99, 143.

Note: When we face such a type of problem, we should be aware of various types of basic patterns like increasing and decreasing, multiplication, division, square, etc. being used in a series formation. Then, with the basic knowledge of those basic patterns, we can understand the new patterns as well.