Answer
Difference between the sum of first 11 terms of $a_{n}$ and the sum of first 11 terms of $b_{n}$ = -28187.5 - (-715) = -27472.5
Work Step by Step
Given sequence
|$a_{n}$| = -5, 10, -20, 40. This is a geometric sequence with common ratio = -2
By $a_{n}$ = a $r^{n-1}$.
$a_{11}$ = (-5) $(-2)^{11-1}$ = (-5) $(-2)^{10}$ = (-5)$\times$(1024) = -5120
The sum of first 11 terms of $a_{n}$ =$\frac{11}{2}$($a_{1}$ +$a_{11}$)
= $\frac{11}{2}$(- 5 -5120 )
= $\frac{11}{2}$$\times$ (-5125) = -28187.5
|$b_{n}$| = 10, -5, -20, -35. This is a arithmetic sequence with common difference = -15
By $b_{n}$ = $b_{1}$ + (n - 1) d.
$b_{11}$ = 10 + (11 - 1) (-15) = 10 - 150 = -140
The sum of first 11 terms of $b_{n}$= $\frac{11}{2}$($b_{1}$ +$b_{11}$)
= $\frac{11}{2}$( 10 - 140 )
= $\frac{11}{2}$(- 130 )
=-715
Difference between the sum of first 11 terms of $a_{n}$ and the sum of first 11 terms of $b_{n}$ = -28187.5 - (-715) = -27472.5
