Question

Describe this pattern and Find the next 3 numbers in the pattern 3.5, 13, 41.5, 127, , , . also explain in a easy way how you find it

Answer 1

You have:

$a_1=3.5,\\ \\a_2=13,\\ \\a_3=41.5,\\ \\a_4=127.$

Find

$a_2-a_1=13-3.5=9.5,\\ \\a_3-a_2=127-41.5=28.5=9.5\cdot 3,\\ \\a_4-a_3=127-41.5=85.5=28.5\cdot 3=9.5\cdot 3^2.$

This gives you the rule how to find next terms:

1.

$a_5-a_4=9.5\cdot 3^3,\\ \\a_5-127=256.5,\\ \\a_5=127+256.5=383.5.$

2.

$a_6-a_5=9.5\cdot 3^4,\\ \\a_6-383.5=769.5,\\ \\a_6=383.5+769.5= 1153.$

3.

$a_7-a_6=9.5\cdot 3^5,\\ \\a_7-1153=2308.5,\\ \\a_7=1153+2308.5=3461.5.$

Answer: next 3 terms are 383.5, 1153 and 3461.5.