Question

if the sum of first n terms of an AP is 4n-4n^2,what is the first term ( S1) what is the sum of first two terms? what is the second term?find 3rd,10th and nth term

Answer 1

Sn = 4n - 4$n^{2}$
Put n = 1
S1 = 4 - 4 
    = 0
Put n = 2
S2 = 4(2) - 4(4)
     = 8 - 16
     = -8
S1 = 0  =>  a = 0 [First term is 0]
S2 = -8  =>  Sum of first two terms = -8
              => a + a2 = -8  =>  a2 = -8  [Second term is -8]
Now,
a = 0, d = -8
an = a + (n - 1)d
a3 = 0 + 2(-8)
     = -16
a10 = 0 + 9(-8)
       = -72
an = 0 + (n - 1)(-8)
     = -8n + 8
     = 8(1 - n)

First term = 0
Sum of first two terms = -8
Second term = -8
Third term = -16
Tenth term = -72
Sum of n terms = 8(1 - n)