Question

Find the next two terms of an A.P. 4, 9, 14, …..

Answer 1

Hint: For an AP series the difference between each presiding term are the same.
The nth term for an Arithmetic Progressive series can be found out by using the formula \[t{}_n = a + \left( {n - 1} \right)d \]
In this question since the first three terms are given so we will first find out their common differences and then we will find the missing terms of the series.

Complete step-by-step answer:
Given
1st Term \[{T_1} = 4 \]
2nd Term \[{T_2} = 9 \]
3rd Term \[{T_3} = 14 \]
In the given series its first three terms are given and since the given series is in AP so we will first find its common difference for its first three terms
 \[d = {T_2} - {T_1} = 9 - 4 = 5 \]
 \[d = {T_3} - {T_2} = 14 - 9 = 5 \]
Hence we can say the common difference of the series is \[d = 5 \]
Now we know the nth term for an Arithmetic Progressive series can be found out by using the formula \[t{}_n = a + \left( {n - 1} \right)d \] , where the first term of the series
 \[{t_1} = a = 4 \]
Now since we have to find the next two term of the series so the 4th term of the series will be
 \[t{}_4 = a + \left( {4 - 1} \right)d - - (i) \]
By substituting the values we get
 \[
 \Rightarrow t{}_4 = 4 + 3 \times 5 \ \
   = 4 + 15 \ \
   = 19 \;
  \]
And also the fifth term of the series will be equal to
 \[t{}_5 = a + \left( {5 - 1} \right)d - - (ii) \]
Hence by substituting the values we get
 \[
 \Rightarrow t{}_5 = 4 + 4 \times 5 \ \
   = 4 + 20 \ \
   = 24 \;
  \]
So the fifth term of the series is 24
Hence from the above observations we can say the 4th term of the given AP series is 19 and its 5th term is 24.
So the next two terms of the series is 4, 9, 14, 19, 24
So, the correct answer is “4, 9, 14, 19, 24”.

Note: Students can determine whether a given series is an Arithmetic series or not by finding the differences between each term of the series and if the differences between each terms are same then the series is an AP series.