Answer:
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;
[tex]S_n = \dfrac{n}{2} \cdot \left [2 \cdot a + (n - 1)\cdot d \right ][/tex]
(47/2)*(2*12+(47-1)*4)
The sum of the first 47 terms is therefore given as follows;
[tex]S_n = \dfrac{47}{2} \cdot \left [2 \times 12 + (47 - 1)\times 4 \right ] = 4,888[/tex]
The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ = 4,888
