Question

The sum of an airthametic series with 15 terms is 180 then the 8th term is

Answer 1

The formula for the sum of an arithmetic series is: 

S = (n/2)(1st + last) 

where n = the number of terms = 15 
1st = 1st term = x 
last = last term = x + (n-1)(d) 

180 = (15/2)(x + x + 14d) 
180 = (15/2)(2x + 14d) 
360/15 = 2x + 14d 
24 = 2x + 14d 
12 = x + 7d 

8th term = x + (8-1)d 
8th term = x + 7d 

as you can see, simplifying the sum of the series gave us that x + 7d was 12, therefore the 8th term is 12 

Answer 2

Answer:

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Step-by-step explanation:

The formula for the sum of an arithmetic series is:

S = (n/2)(1st + last)

where n = the number of terms = 15

1st = 1st term = x

last = last term = x + (n-1)(d)

180 = (15/2)(x + x + 14d)

180 = (15/2)(2x + 14d)

360/15 = 2x + 14d

24 = 2x + 14d

12 = x + 7d

8th term = x + (8-1)d

8th term = x + 7d

as you can see, simplifying the sum of the series gave us that x + 7d was 12, therefore the 8th term is 12

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