nth term of an AP

[Guest]

The sum of first m terms of an AP is [tex]4m^2 - m[/tex].
If its nth term is 107, find the value of n.

[Jonasmathwork]

Given s_m = 4m^2 - m

Let us take the values of m = 1, 2, 3, .....

m = 1 => 4.1^2 - 1 = 3
m = 2 => 4.2^2 - 2 = 14
m = 3 => 4.3^2 - 3 = 33
--------------------

Now let us find the values of sequence

First term, a_1 = s_1 = 3
Second term, a_2 = s_2 - s_1 = 11
Third term, a_3 = s_3 - s_2 = 19
---------------------

=> AP is 3, 11, 19 , ----
Here a_1 = 3 & d = 11 - 3 = 8
where a_1 is first term & d is the common difference

Again, we know a_n = 107
i.e. a_1 + (n - 1)d = 107
=> 3 + (n - 1)8 = 107
=> 3 + 8n - 8 = 107
=> 8n = 112
or n = 14