Question

Find the 12th term of AP: 9,13,17,21…….

Answer 1

Hint: We have to find to find 12^th term of a given AP: 9,13,17,21……., we first write the general series of AP and compare each and every term with the given AP and find the corresponding values of first term(a), common difference (d) and nth term of AP. After it we will come to know that formula for nth Term of AP is
 \[a+(n-1)d\] and here \[a=9\], \[d=13-9=4\] and \[n=12\].

Complete step-by-step answer:
We are given an AP: 9,13,17,21……. And we have to find its 12th term so for that we can assume any general AP which can be written as \[a,a+d,a+2d,a+3d.......a+(n-1)d\] , so we can see that first term of AP is a , common difference is d and the \[{{n}^{th}}\]term of AP as clearly visible is \[a+(n-1)d\]
So comparing this AP we given AP we get \[a=9\] , d is the difference between any two consecutive terms so considering 2nd and 1st first \[d=13-9=4\] and we have to find 12th term means we can put \[n=12\], so on applying formula \[a+(n-1)d\]our 12th term will be
\[9+(12-1)\times 4\] which on solving looks \[9+(11)\times 4\] on further solving gives \[9+44\] which finally equals to 53
Hence the 12th term of given AP is 53.

Note: If we are asked to find the sum of the first 12 terms of AP: 9,13,17,21…….
For that we have a formula for sum of AP of n terms which is given by
\[sum=\dfrac{n}{2}\times (2a+(n-1)\times d)\] we know the values of all the constants in formula as
 \[a=9\], \[n=12\],\[d=4\] putting these values in formula we get
\[sum=\dfrac{12}{2}\times (2\times 9+(12-1)\times 4)=6\times (18+44)\]
Which finally equals 372.