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
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.