Let S_{n }be the sum of the first n terms of the series 1^{2 }+ 2.5^{2} + 3^{2} + 2.7^{2} + 5^{2} + 2.9^{2 }+... if S_{20} = 20A then A is equal to

a) 2001

b) 2019

c) 1851

d) 1951

e) None of these

Please provide an explanation as well.

amygdaleon305 Apr 19, 2021

#1**+3 **

Firstly, this is not really the sum of 1 sequence, it is the sum of 2 sequences

\(1^2+3^2+5^2+ .......\\ 2.5^2+2.7^2+2.9^2......\\ S_{20}=1^2+3^2+5^2+ .......+19^2\quad+ \quad 2.5^2+2.7^2+2.9^2......+4.3^2\)

I suppose I could just calculate the answer.

\(S_{20}=1330+118.9 = 1448.9\\ A=1448.9/20=72.445\)

Doesn't look like any of those answers to me.

Melody Apr 19, 2021