Question

if the sum of the first n terms of an Ap is 4n-n2 what is first term? what is the sum of first two terms? what is the second term? similarly find the 3rd and 10th and nth terms

Answer 1

We have been given ,
Sn = 4n -n^2

Just Think The Given Equation Of The Sum Of " n " Terms Is correct for all the terms in the AP , So If you put n=1 You get Sum of 1 terms which is actually the value of first term a1 .
It goes like this ,
Sn = 4n - n^2
= 4(1) - (1)^2
= 4 - 1 = 3

so The First Term Is 3.

Sum Of 2 Terms Is ...
S2 = 4(2) - (2)^2 = 4

Sum of first 2 Terms means a1 + a2 ,
Now you know a1 and S2 , so S2 - a1 = a2 = 4-3= 1

Now the common difference ,
a2- a1 = d = 1-3 = -2.

Hence The Basic Method Of Doing That was this .

Solving for a10 , an , a3 we get ,
a3 = -1 ;
a10 = -15;
an = 5 - 2n ;

That's It !

Answer 2

an=5-2n
find it using an formula