Answer
Difference between the sum of first 15 terms of $b_{n}$ and the Sum of first 15 terms of $a_{n}$ = 570 -(- 405) = 570 + 405 = 975
Work Step by Step
From graph
First term $a_{1}$ = 1
Second term $a_{2}$ = -3
Third term $a_{3}$ = -7
Common difference (d) = -7 + 3 = -3 - 1 = -4
$15^{th}$ term $a_{15}$ = 1 + (15 - 1)(-4) = 1 - 56 = -55
Sequence = 1, -3, -7, . . . . . -55
Sum of first 15 terms of $a_{n}$ = $\frac{15}{2}$(1 - 55) = $\frac{15}{2}$(- 54) = 15$\times$(-27) = -405
From graph
First term $b_{1}$ = 3
Second term $b_{2}$ = 8
Third term $b_{3}$ = 13
Common difference (d) = 13 - 8 = 8 - 3 = 5
$15^{th}$ term $b_{15}$ = 3 + (15-1)5 = 3 + 70 = 73
Sequence = 3, 8, 13, . . . . . 73
Sum of first 15 terms of $b_{n}$ = $\frac{15}{2}$(3 + 73) = $\frac{15}{2}$(76) = 15$\times$38 = 570
Difference between the sum of first 15 terms of $b_{n}$ and the Sum of first 15 terms of $a_{n}$ = 570 -(- 405) = 570 + 405 = 975