How do you find the sum of the arithmetic sequence given d= -4, an = 27, and n = 9?

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Answer 1 · 2016-05-25T16:15:32

The sum of the terms of the progression:
# =color(blue)( 387#

The common difference: #d =- 4#

The/ last term: #a_n = 27#

The number of terms: #n =9#

Applying the formula:
#color(blue)(a_n = a_1 + (n-1)d#, we can obtain the first term #(a_1)# of the series.

#27 = a_1 + (9-1) xx (-4)#

#27 = a_1 + (8) xx (-4)#

#27 = a_1 -32#

# a_1 = 27 + 32#

# a_1 = 59#

Now, we calculate the sum using formula:
#color(green)(S_n = n/2 (a_1 + a_n)#

#S_n = 9/2 ( 59 + 27)#

#S_n = 9/2 ( 86)#

#S_n = 9/cancel2 ( cancel86)#

#S_n = 9 * 43#

#S_n = 387#