Question

In an A.P,the sum of its first n term is 6n-n².Find its 25th term

Answer 1

$S_n = 6n - n^2$
we know that ,
     $T_n =S_n - S_{n-1}$
so, 
[tex]T_n = 6n - n^2 -[6(n - 1) -(n - 1)^2] \\ =6(n - n + 1) - (n^2 - n^2 + 2n - 1) \\ =7 -2n [/tex]
$T_{25} = 7 - 2*25 \\ = 7 - 50 \\ = -43$

Answer 2

Hi !
Sn = 6n - n²

S₁ = 6(1) - 1² = 6 -1 = 5
S₂ = 6(2) - 2² = 12 - 4 = 8
S₃ = 6(3) - 3² = 18 -9 = 9

First term = a₁ = S₁ = 5
Second term = a₂ = S₂ - S₁ = 8 - 5 = 3
Third term = S₃ - S₂ = 9 - 8 = 1

The A.P is 5,3,1 .....

First term = a = 5
Common difference = -2

We have to find 25th term :-

a₂₅ = a + 24d

5 + 24 (-2) = -43

-43 is the 25th term