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The th term of an increasing linear sequence

The th term of an increasing linear sequence.

  • Find the common difference between consecutive terms.
  • Start with that difference multiplied by , then find the constant adjustment.
  • Check the rule using several positions. The first term is at .

Example 1

Find an expression for the th term. The first term has position .

A constant first difference means the rule is linear.Compare the first term with when .Check that the rule gives all four displayed terms.

Example 2

Find an expression for the th term. The first term has position .

A constant first difference means the rule is linear.Compare the first term with when .Check that the rule gives all four displayed terms.

Your turn

Question 1

Find an expression for the th term. The first term has position .

Check answer
A constant first difference means the rule is linear.Compare the first term with when .Check that the rule gives all four displayed terms.
Question 2

Find an expression for the th term. The first term has position .

Check answer
A constant first difference means the rule is linear.Compare the first term with when .Check that the rule gives all four displayed terms.
Question 3

Find an expression for the th term. The first term has position .

Check answer
A constant first difference means the rule is linear.Compare the first term with when .Check that the rule gives all four displayed terms.
Question 4

Find an expression for the th term. The first term has position .

Check answer
A constant first difference means the rule is linear.Compare the first term with when .Check that the rule gives all four displayed terms.
Question 5

Find an expression for the th term. The first term has position .

Check answer
A constant first difference means the rule is linear.Compare the first term with when .Check that the rule gives all four displayed terms.
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