Question

Explain the rule for finding the next term in the sequence.
Find the next three terms in the sequence

a) 1,1.5,2,2.5

(Show with working)

Use formula- a1+(n-1)d

Answer 1

The rule for finding the next term in the sequence is to add a constant difference (d) to the previous term.

a) 1, 1.5, 2, 2.5...

To find the constant difference, we subtract any term from its preceding term.

d = 1.5 - 1 = 0.5

Now we can use the formula:
an = a1 + (n-1)d

where an is the nth term in the sequence, a1 is the first term, n is the position of the term we want to find.

To find the next term, n = 5:

a5 = 1 + (5-1)0.5
a5 = 1 + 2(0.5)
a5 = 2

To find the next three terms, we continue adding 0.5 to each term:

a6 = 2.5 + 0.5 = 3
a7 = 3 + 0.5 = 3.5
a8 = 3.5 + 0.5 = 4

Therefore, the next three terms in the sequence are: 2, 3, 3.5, 4.