Question

Find the next two terms of the sequence: 80, −40, 20, −10, ______, ______.

Answer 1

To find the next two terms of the sequence: 80, −40, 20, −10, we can first look at the pattern in the sequence.

1. From 80 to -40:
The change is -120 (80 - 120 = -40).

2. From -40 to 20:
The change is +60 (-40 + 60 = 20).

3. From 20 to -10:
The change is -30 (20 - 30 = -10).

Now we can summarize the changes as follows:
- First change: -120
- Second change: +60
- Third change: -30

Observing these changes:
-120, +60, -30
The pattern seems to be that each change is halving the absolute value of the previous value. After -120, +60, and -30, we can anticipate the changes will continue in a similar halving manner.

So we could predict the next change (after -30) as:
-15 (halving -30)

Thus, the next term would be:
-10 - 15 = -25

Now for the subsequent change after -15, we can expect:
+7.5 (halving -15)

So the next term after -25 would be:
-25 + 7.5 = -17.5

Thus, the next two terms in the sequence are:
-25 and -17.5.

So, the complete sequence now reads:
80, −40, 20, −10, −25, −17.5.