Only 1% Can Solve This Tricky Arithmetic Sequence Puzzle! Can You? #riddlemathworld #hopoe

"Only 1% Can Solve This Tricky Arithmetic Sequence Puzzle! Can You?"

"Think you’re good at arithmetic sequences? Prove it! 🧠 This seemingly simple puzzle will challenge your number-crunching skills. Can you calculate the sum of the first 10 terms in a sequence that starts at 5 and increases by 3? Drop your answer in the comments, challenge your friends, and don’t forget to like, subscribe, and hit the bell for more brain-busting math puzzles!"

Only 1 in 100 Can Solve This Tricky Arithmetic Sequence Puzzle! Are You One of Them?
Question:
A sequence starts at 5 and increases by 3. What is the sum of the first 10 terms of this sequence?
Options:
A) 155
B) 170
C) 185
D) 200
________________________________________
Answer:
The correct answer is B) 170.
Explanation:
• Step 1: Identify the sequence:
The first term (aa) = 5
Common difference (dd) = 3
Number of terms (nn) = 10
• Step 2: Find the nn-th term using the formula:
an=a+(n−1)×da_n = a + (n-1) \times d a10=5+(10−1)×3a_{10} = 5 + (10-1) \times 3 a10=5+27=32a_{10} = 5 + 27 = 32
• Step 3: Sum of the first nn terms using the formula:
Sn=n2[2a+(n−1)×d]S_n = \frac{n}{2} [2a + (n-1) \times d] S10=102[2×5+(10−1)×3]S_{10} = \frac{10}{2} [2 \times 5 + (10-1) \times 3] S10=5[10+27]S_{10} = 5 [10 + 27] S10=5×37=185S_{10} = 5 \times 37 = 185
• However, since the calculation of the sum includes a step where the common difference was incorrectly calculated, the correct answer should be verified:
The correct sum calculation is:
S10=5[2×5+(9)×3]S_{10} = 5 [2 \times 5 + (9) \times 3] S10=5[10+27]S_{10} = 5 [10 + 27] S10=5×37=185S_{10} = 5 \times 37 = 185
The correct answer is C) 185.
Logical Twist:
The tricky part here is accurately calculating the sum by correctly applying the formula, especially ensuring that the common difference is correctly accounted for in the final calculation.
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