Question

In a sequence of numbers the first number is 3 and each number after the first is 2 more than 3 times the preceding number. What is the fourth term in the sequence?
$
  (a){\text{ 105}} \\
  (b){\text{ 106}} \\
  (c){\text{ 107}} \\
  (d){\text{ 108}} \\
$

Answer 1

Hint: In this question the first number is given to us, and the relation between every next number and its preceding number is also given to us. Use this relation to find the fourth number of this sequence.

Complete step-by-step answer:

Let the first number be x.
Now it is given that each number after the first is 2 more than 3 times the preceding number.
So construct the linear equation according to given information.
Let the next number be y.
So y is equal to 3 times x plus 2.
$ \Rightarrow y = 3x + 2$ ( y is second number)
Now it is given first number is 3 so x=3
So the second number =$\left( {3 \times 3 + 2} \right) = 9 + 2 = 11$.
Now in place of x substitute 11 and calculate the value of the third number.
So third number = $\left( {3 \times 11 + 2} \right) = 33 + 2 = 35$
Now in place of x substitute 35 and calculate the value of the fourth number.
So fourth number = $\left( {3 \times 35 + 2} \right) = 105 + 2 = 107$
So, this is the required fourth number.
Hence option (c) is correct.

Note: Whenever we face such types of problems the key concept is to understand the given relationship between the term and its preceding term. One note point here is that since every term has dependence over its previous term therefore the fourth term can’t be evaluated without evaluating the third term so follow up the pattern, this will help in getting the right track to reach the answer.