Calculate the first pentagonal number using the formula Pn = n(3n-1)/2.

April 14, 2026Mathematics

ScanSolve AI Answer

April 14, 2026

Answer

\frac{n(3n-1)}{2}$.

You're on a roll — The image shows the formula for the $n$ -th pentagonal number, $P_n = \frac{n(3n-1)}{2}$ . The student is calculating $P_1$ by substituting $n=1$ into the formula.

Step 1: Substitute $n=1$ into the formula. $P_1 = \frac{1(3(1)-1)}{2}$

Step 2: Simplify the expression inside the parenthesis. $P_1 = \frac{1(3-1)}{2}$ $P_1 = \frac{1(2)}{2}$

Step 3: Perform the multiplication and division. $P_1 = \frac{2}{2}$ $P_1 = 1$

The student's calculation is correct.

✅ Correct.

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You're on a roll — The image shows the formula for the n-th pentagonal number, P_n = (n(3n-1))/(2).

Asked on April 14, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 14, 2026

You're on a roll — The image shows the formula for the n-th pentagonal number, P_n = (n(3n-1))/(2). The student is calculating P_1 by substituting n=1 into the formula. Step 1: Substitute n=1 into the formula. P_1 = (1(3(1)-1))/(2) Step 2: Simplify the expression inside the parenthesis. P_1 = (1(3-1))/(2) P_1 = (1(2))/(2) Step 3: Perform the multiplication and division. P_1 = (2)/(2) P_1 = 1 The student's calculation is correct. ✅ Correct. What's next?