Name the term

The idea

t₁, t₂, t₃, … denote the first, second, third … terms of a sequence, with the subscript matching the position; other letters such as s or u name other sequences, and terms can be any real number.

A short name

Talking about "the third number in the list" gets long. Mathematicians use short names: t₁, t₂, t₃, …

For the odd numbers 1, 3, 5, 7, 9, … what do you think t₄ means?

• The 4th term
• 4 times t
• The number 4

Find the named term

Each row is a sequence. Tap a card to see its name. Then find the term the task asks for.

The little number

t₁, t₂, t₃, … denote the first, second, third … terms of a sequence. The subscript matches the position. Other letters such as s or u name other sequences, and terms can be any real number.

t₄ = 7 tells us that the term in the fourth position is 7.

The position n is a whole number, but the term itself can be negative or a fraction: s₁ = −7 in the sequence −7, −3, 1, 5, 9, …

Notes

t₁, t₂, t₃, … denote the first, second, third … terms; the subscript matches the position. Other letters (s, u, …) name other sequences, and terms can be any real number.

Check yourself

In the odd numbers 1, 3, 5, 7, 9, 11, … what is t₃?

A sequence s is −7, −3, 1, 5, 9, … What is s₄?

Answer: 5

The terms are s₁ = −7, s₂ = −3, s₃ = 1, s₄ = 5.

In some sequence t₇ = 13. What does that tell us?

Can a term of a sequence be negative, like s₁ = −7?

• 3. 3 is t₂, the second term. The little number is the position, so t₃ is the third term.
• 5 — correct. Yes. The third term is 5, so t₃ = 5.
• 7. 7 is t₄, the fourth term. Count 1, 3, 5: the third is 5.
• The term in the 7th position is 13 — correct. Yes. The subscript 7 is the position, and 13 is the term in it.
• The 13th term is 7. It is the other way round. The little number is the position, so 7 is the position and 13 is the term.
• t multiplied by 7 is 13. The little 7 is not a multiplier. It tells us the position of the term.
• No. Terms must be positive.. The book shows the sequence −7, −3, 1, 5, 9, … whose first term s₁ is −7.
• Yes. The position n is a whole number, but the term can be negative, a fraction or any real number. — correct. Yes. The sequence −7, −3, 1, 5, 9, … has a negative first term.
• Only if the position is negative too.. The position stays a whole number. The term can be negative whatever the position.