Question

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

12, 16. 20. ...

Answer 1

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

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;

`S_n = (n)/(2) \cdot \left [2 \cdot a + (n - 1)\cdot d \right ]`

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

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

`S_n = (47)/(2) \cdot \left [2 * 12 + (47 - 1)* 4 \right ] = 4,888`

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