Find the sum of the first 47 terms of the following series, to the nearest integer. 12, 16. 20. ...

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ is 4,888

Step-by-step explanation:

The given series is;

12, 16, 20, ...,

Therefore, the first term of the series is, a = 12

The common difference of series is found as follows;

The difference between subsequent terms, 12 and 16 is  16 - 12 = 4

The difference between subsequent terms, 16, and 20 is  20 - 16 = 4

Therefore, the common difference, d = 4

The series is therefore an arithmetic projection, AP

The sum of the first 'n' terms of an AP, Sₙ, is given as follows;

(47/2)*(2*12+(47-1)*4)

The sum of the first 47 terms is therefore given as follows;

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ = 4,888

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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