Answer
Difference between the sum of first 10 terms of $a_{n}$ and the sum of first 10 terms of $b_{n}$ = 13350
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 $r^{n-1}$.
$a_{10}$ = (-5) $(-2)^{10-1}$ = (-5) $(-2)^{9}$ = (-5)$\times$(-512) = 2560
The sum of first 10 terms of $a_{n}$ = $\frac{10}{2}$($a_{1}$ +$a_{10}$ )
= $\frac{10}{2}$(- 5 + 2560 )
= 5 $\times$ 2555 = 12775
|$b_{n}$| = 10, -5, -20, -35. This is a arithmetic sequence with common difference = -15
By $b_{n}$ = $b_{1}$ + (n - 1) d.
$b_{10}$ = 10 + (10 - 1) (-15) = 10 - 135 = -125
The sum of first 10 terms of $b_{n}$ = $\frac{10}{2}$($b_{1}$ +$b_{10}$ )
= $\frac{10}{2}$(-125 + 10 )
= 5 $\times$ (-115) = -575
Difference between the sum of first 10 terms of $a_{n}$ and the sum of first 10 terms of $b_{n}$ = 12775 - (-575) = 13350
