Based on the pattern, what are the next two terms of the sequence 9, 15, 21, 27, ...?

2 Answers
Mar 8, 2017

Answer:

#33, 39#

Explanation:

Let's look at the sequence term by term:

#a_1 = 9#
#a_2 = 15#
#a_3 = 21#

Notice that: #a_2 -a_1 =6# and #a_3 - a_2 =6#

We can deduce that: #a_"n+1" = a_n + 6#

We can test this on the #4^(th)# term: #a_4# should equal #21+6 = 27#

Since this checks out we can say that the sequence is an arithmetic progression with a common diference of 6.

#:. a_5 = 27+ 6 = 33#

and

#a_6 =33+6 = 39#

Mar 10, 2017

Answer:

#33" , "39#

Explanation:

When you are presented with a sequence of numbers which you have to continue, there are different possibilities to consider.....

  • Ask yourself whether the numbers are a specific type of number?

#1, 3, 5, 7, ...# would be odd numbers.
#1, 4, 9, 16 ....# would be square numbers.
#2,3, 5, 7, 11 ....# would be prime numbers
#7, 14, 21, 28, ....# would be multiples of 7.

If you recognise a that a certain type of number has been given you can easily fill in the next terms.

  • Ask whether there is a term-to-term rule which you can use to get from one term to the next.
  • This is often by adding or subtracting the same number each time, this gives an Arithmetic Sequence. (A.P.)
  • It can be by multiplying or dividing by the same number each time, this gives a Geometric Sequence. (G.P.)
  • Maybe adding on the previous term gives the next term. This is called a Fibonacci sequence.

  • Has a rule been given for the #n^("th") # term? Like #T_n = n^2/(n+1)#?
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In this case we have #9, 15, 21,27 .....#

You should see that the term-to-term rule is "add 6"
#color(white)(...)color(red)(+6rarr)" "color(red)(+6rarr)" "color(red)(+6rarr)" "color(red)(+6rarr)#
#9," " 15," " 21," "27" " #

So, following this pattern gives the next 2 terms as #33 and 39#