Question

Find the 17th term of the AP: $4,9,14...............$

Answer 1

Hint: In order to find out the 17th term we will use the basic formula of nth term of A.P. which is given as ${a_n} = a + \left( {n - 1} \right)d$ where $a$ is the first term and d is the common difference.

Complete step-by-step solution:

Given A.P. is $4,9,14...............$
So, here first term is $a = 4$
Now, we will find the common difference
   $
  \therefore d = {a_2} - {a_1} \\
  {\text{here }}{{\text{a}}_2} = 9{\text{ and }}{{\text{a}}_1} = 4 \\
  d = 9 - 4 \\
  d = 5 \\
  $
We know that the nth term of A.P is given as
${a_n} = a + \left( {n - 1} \right)d$
For the seventeenth term we have to put the value of n as 17
$
  {a_{17}} = a + \left( {17 - 1} \right)d \\
  {a_{17}} = a + 16d \\
  $
Substituting the value of a and d, we get
$
   \Rightarrow {a_{17}} = a + 16d \\
   \Rightarrow {a_{17}} = 4 + 16 \times 5 \\
   \Rightarrow {a_{17}} = 4 + 80 \\
   \Rightarrow {a_{17}} = 84 \\
  $
Hence, the value of the 17th term of the A.P. is 84.

Note: In order to solve these types of problems, first of all remember the formula of arithmetic progression. Remember how to find the nth term of and A.P. Also remember how to find the sum of n terms of an A.P. Similarly learn about geometric progression and harmonic progression. This will help a lot to solve problems related to A.P, G.P and H.P.