Question

show that the sum of n terms of the series (4+12+20+28+......) is the square of an even number

Answer 1

this series is in AP
so, first term( a) = 4
common difference(d) = 8
sum of nth term = n/2{ 2a + ( n -1)d }

Sn = n/2{ 8 + ( n -1)8} = 4n

you can see that sum of nth numbers of this series = 4n ( even number )

Answer 2

given, series 4+12+20+28+.......................

is in arthimetic progression


a=4

d=8

sum to n terms of an a.p is

n/2(2(4)+(n-1)8)

=n(4+4n-4)

=n(4n)=4n²which is divisible by 2

so it is even number



I hope this will help u:)