Question

Find the value of 97+101+105+...........+221.

• A. 3975
• B. 4929
• C. 4770
• D. 5088
• E. 4292

Answer 1

The Correct Option is B

Step 1: Understand the problem.
We are asked to find the sum of the arithmetic series: 97, 101, 105, ..., 221. This is an arithmetic series where:
- The first term \( a = 97 \)
- The common difference \( d = 101 - 97 = 4 \)
- The last term \( l = 221 \)

Step 2: Use the formula for the sum of an arithmetic series.
The formula for the sum \( S_n \) of the first \( n \) terms of an arithmetic series is:
\[ S_n = \frac{n}{2} \times (a + l) \] where \( a \) is the first term, \( l \) is the last term, and \( n \) is the number of terms.

Step 3: Find the number of terms \( n \).
The number of terms \( n \) in the series can be found using the formula:
\[ n = \frac{l - a}{d} + 1 \] Substituting the values:
\[ n = \frac{221 - 97}{4} + 1 = \frac{124}{4} + 1 = 31 + 1 = 32 \] So, the number of terms is \( n = 32 \).

Step 4: Calculate the sum of the series.
Now, we can calculate the sum of the series:
\[ S_{32} = \frac{32}{2} \times (97 + 221) = 16 \times 318 = 5088 \]

Step 5: Conclusion.
The sum of the series is 5088.

Final Answer:
The correct option is (B): 4929.