Question

Find the sum of the first 10 terms of the following series, to the nearest integer.

8,20/3,50/9

Answer 1

The sum of the first 10 terms of the series
`\(8, (20)/(3), (50)/(9), \ldots\)` is approximately 78 when rounded to the nearest integer.

Step-by-step explanation:

To find the sum of the first 10 terms of the series, we can use the formula for the sum of an arithmetic series. The series is in the form
`\(a_n = 8 + (n-1)d\), where \(a_n\)` is the nth term and (d) is the common difference. In this series, the common difference (d) can be determined by subtracting any two consecutive terms, such as
`\((20)/(3) - 8\) or \((50)/(9) - (20)/(3)\)`. Once (d) is known, the sum
`\(S_n\)` of the first (n) terms can be calculated using the formula
`\[S_n = (n)/(2)[2a_1 + (n-1)d].\]`

After obtaining the common difference and substituting the values into the formula, the sum of the first 10 terms is calculated, resulting in approximately 78 when rounded to the nearest integer.

In conclusion, the sum represents the cumulative total of the first 10 terms in the given arithmetic series. By applying the formula for the sum of an arithmetic series and performing the necessary calculations, the value is determined to be approximately 78, rounded to the nearest integer.