Question

Which describes the pattern in the sequence shown?

3,7,15,31...
Multiply a term by 3 and subtract 2 to get to the next term
Add 4 to a term to get the next term
Each Term is the sum of the two preceding terms plus 5
O Multiply a term by 2 and add 1 to get the next term

Answer 1

multiply a term by 2 and add 1 to get the next term

Explanation:

3×2=6 +1 =7

7×2=14+1= 15

15×2=30+1=31

Answer 2

Multiply a term by 2 and add 1 to get the next term

Explanation:

The first differences of terms are ...

7 -3 = 4

15 -7 = 8

31 -15 = 16

We notice that these increase by a factor of 2. This signifies an exponential sequence. That factor (2) will be the value that each term is multiplied by to get the next. This eliminates the choices "add 4" and "multiply a term by 3 ...".

Trying the remaining two choices, we find that the one that fits is the one shown above.

3+7 ≠ 15, so "the sum of the two preceding terms" doesn't work

2(3) +1 = 7; 2(7) +1 = 15; 2(15) +1 = 31, so "multiply by 2 and add 1" works fine