Find the sum of the first 32 terms of the arithmetic sequence 24, 20, 16,

= - 1216

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

= [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 24 and d = a₂ - a₁ = 20 - 24 = - 4 , then

= [ (2 × 24) + (31 × - 4) ]

     = 16(48 - 124)

     = 16 × - 76

     = - 1216

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

no

step-by-step explanation: