the sum of the first nine terms of an arithmetic series is 162, and the sum of the first 12 terms is 288. Determine the first five terms of the series.

Step-by-step explanation:

Given that , the sum of the first nine terms of an arithmetic series is 162 and the sum of the first 12 terms is 288.

• The sum of n terms of an AP is

• nth term of an AP is given by ,

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.