Next terms and the rule questions with answers

Questions

1. Question 1Common difference: the next term

   Write down the next term of the sequence $-3, \ -9, \ -15, \ -21, \ \ldots$.

   Show the worked solution

   1. Step 1: Find the common difference: a term minus the one before it$\mathstrut -9 - (-3) =$ $-6$
   2. Step 2: Add the difference to the last term$\mathstrut -21 + (-6) =$ $-27$
2. Question 2A missing term

   Find the missing term in the sequence $5, \ 2, \ \_\_\_, \ -4, \ -7$.

   Show the worked solution

   1. Step 1: Find the common difference: a term minus the one before it$\mathstrut 2 - 5 =$ $-3$
   2. Step 2: The missing term is the one before it plus the difference$\mathstrut 2 + (-3) =$ $-1$
3. Question 3Multiplying sequences

   Write down the next term of the sequence $4, \ -8, \ 16, \ -32, \ \ldots$.

   Show the worked solution

   1. Step 1: How does each term change from the one before it?The differences are not equal: each term is the one before it multiplied by the same number.
   2. Step 2: Divide a term by the one before it$\mathstrut (-8) \div 4 =$ $-2$
   3. Step 3: Multiply the last term by the same number$\mathstrut (-32) \times (-2) =$ $64$
4. Question 4Growing differences and square numbers

   Write down the next term of the sequence $25, \ 36, \ 49, \ 64, \ \ldots$.

   Show the worked solution

   1. Step 1: Find the differences between the terms$\mathstrut 36 - 25 =$ $11$$\mathstrut 49 - 36 =$ $13$$\mathstrut 64 - 49 =$ $15$
   2. Step 2: Find how the differences change, then the next difference$\mathstrut 13 - 11 =$ $2$$\mathstrut 15 + 2 =$ $17$
   3. Step 3: Add it to the last term$\mathstrut 64 + 17 =$ $81$