The sum of every five numbers in the number patten below forms a new number pattern. 3, 9, 15, 21, 27, . . .
Write the first three numbers in the new pattern and describe the pattern.

9514 1404 393

Step-by-step explanation:

The original pattern has a first term of a1=3 and a common difference of d=6.

The sum of the first 5 numbers in the pattern is ...

  Sn = (2·a1 +d(n -1))(n/2)

  S5 = (2·3 +6·4)(5/2) = 75

The common difference is 6, so each of the numbers in the next five of the sequence will be 5·6 = 30 more than in the previous group. The sum of numbers in that group will be 30·5 = 150 more than the sum in the previous group.

So, the new number pattern has a first number of 75 and a common difference of 150. Its first three numbers are 75, 225, 375.