Use the graphs of the arithmetic sequences an and bn to find

Use the graphs of the arithmetic sequences (a_n) and (b_n) to find the difference between the sum of the first 16 terms of {b_n} and the sum of the first 16 terms of (a_n). The difference is 648

Solution

By the graph, for b_n sequence : a = 2 and d = 6 , so, b_n = 2 + 6(n-1)

For a_n sequence : a = 2 and d = -4 , so, a_n = 2 - 4(n-1)

Now, in b_n sequence : S₁₆ = n(a+a_n)/2 = 16[2+2+6(15)]/2 = 8*94= 752

In a_n sequence : S₁₆ = 16[2+2-4(15)]/2 = -8*56 = -448

Difference between them = 752 - (-448) = 752 + 448 = 1200