Use the appropriate formula to find the indicated figurate number.
-the 6th pentagonal number
A) $\mathrm { P } _ { 6 } = 21$
B) $\mathrm { P } _ { 6 } = 36$
C) $\mathrm { P } _ { 6 } = 57$
D) $\mathrm { P } _ { 6 } = 51$

Question

Quizplus · Accepted Answer

The formula for the nth pentagonal number is $\mathrm { P } _ { n } = \frac{3n^2 - n}{2}$. Substituting $n = 6$ gives $\mathrm { P } _ { 6 } = \frac{3(6)^2 - 6}{2} = \frac{108 - 6}{2} = \frac{102}{2} = 51$.

Use the Appropriate Formula to Find the Indicated Figurate Number P6=21\mathrm { P } _ { 6 } = 21P6​=21

Use the Appropriate Formula to Find the Indicated Figurate Number $\mathrm { P } _ { 6 } = 21$