Institution: জাতীয় কবি কাজী নজরুল ইসলাম বিশ্ববিদ্যালয় (JKKNIU) Exam: গ ইউনিট || জাতীয় কবি কাজী নজরুল ইসলাম বিশ্ববিদ্যালয় || 2013
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

The problem asks us to find the sum of a series of numbers from 99 down to 40. This series can be represented as an arithmetic series where the first term (a) is 99, the last term (l) is 40, and the common difference (d) is -1 (since we are counting down).

To calculate the sum of an arithmetic series, we first need to determine the number of terms (n) in the series. The formula for calculating the number of terms in an arithmetic series is:

\[ n = \frac{(l - a)}{d} + 1 \]

Substituting our values:

\[ n = \frac{(40 - 99)}{-1} + 1 = \frac{-59}{-1} + 1 = 59 + 1 = 60 \]

Now that we have 60 terms, we can use the formula for the sum (S) of an arithmetic series:

\[ S = \frac{n}{2} \times (a + l) \]

Substituting the values:

\[ S = \frac{60}{2} \times (99 + 40) = 30 \times 139 = 4170 \]

Thus, the correct answer is option C) ৪১৭০. This method systematically confirms the calculations by using the properties of arithmetic sequences, giving us confidence in the result.