Question

Find the sum to n terms of the series: (33-23)+(53-43)+(73-63)+.....

Answer 1

Answer:

10 × n.

Step-by-step explanation:

Given,

First Term = 33-23=10

Common Difference=(53-43)-(33-13)

=10-10=0.

Sn=

$\frac{n}{2 } \times {2a + (n - 1)d}$

=n/2×{ 2×10 + ( n-1 )0}

=n/2×{ 20 + 0}

=n/2×20

=10×n.

Answer 2

Answer:

4960

Step-by-step explanation:

(3 ^3 −2^3 )+(5 ^3 −4^3 )+...+(21^3 −20 ^3 )

=(3−2)(3^2 +6+2^2 )+(5−4)(5^2 +20+4^2)+...+(21−20)(21^2+420+20^2)

=2^2+3^2+...+21^2 +(2^2+2)+(4^2+4)+..+(20^2+20)

=21×22×43/6 −1+4(1+2^2+3+...+10^2 )+2(1+2+...+10)

=3311−1+4( 10*11*21/6)+ 10*11

=3311−1+1540+110

=4960