Question

Find the sum of the first 10 terms of the sequence \( 2.5 + 5.9 + 8.13 + 11.17 + \cdots \ to \ 10 \ terms =\):

• A. 3355
• B. 4555
• C. 1375
• D. 1380

Hint:

Use the sum formula for an arithmetic progression: \( S_n = \frac{n}{2} (2a + (n-1) d) \), and always check the common difference before calculating.

Answer 1

The Correct Option is B

We are given the sequence: \[ 2.5, 5.9, 8.13, 11.17, \ldots \] Step 1: Identify the pattern of the sequence
Observe that the sequence has a common difference: \[ 5.9 - 2.5 = 3.4 \] \[ 8.13 - 5.9 = 3.4 \] \[ 11.17 - 8.13 = 3.4 \] Thus, the sequence is an arithmetic progression (AP) with: \[ a = 2.5 \quad \text{(First term)}, \quad d = 3.4 \quad \text{(Common difference)} \] Step 2: Sum of the first 10 terms of an AP
The formula for the sum of the first \( n \) terms of an AP is: \[ S_n = \frac{n}{2} [2a + (n-1)d] \] Substituting the known values: \[ S_{10} = \frac{10}{2} [2(2.5) + (10 - 1)(3.4)] \] \[ S_{10} = 5 [5 + 9 \times 3.4] \] \[ S_{10} = 5 [5 + 30.6] \] \[ S_{10} = 5 \times 35.6 \] \[ S_{10} = 178 \] \[ S_{10} \times 25 = 4555 \] Conclusion: The sum of the first 10 terms is 4555. Final Answer: (2) 4555