Pentagonal Numbers - How To Proceed?

if we go from nth figure to (n+1)th figure,it will be 4+3(n-1)

Each pentagonal number has 3 more dots more than the previous one. Thus, if the second pentagonal number has 4 additional dots, then the third has 7, the fourth has 10 and the fifth has $\boxed{13}$ .

You can check again the first problem of this set. From figure 1 to figure 4, there is a pattern you can caught like this.

Fig. 1 : $1$ dot

Fig. 2: $1 + (4$ dot)

Fig. 3: $1 + 4 + (7$ dot)

Fig. 4: $1 + 4 + 7 + (10$ dot)

Dot pattern is the difference of sequence, the different consecutive sequence (Figure) is $3$ dot.

So, Fig. 5: $1 + 4 + 7 + 10 + (13$ dot)