Name and number the terms of a sequence

The first value is labelled t₀. For 9, 13, 17, what is t₁?

This sequence starts at −3 and adds 2. Move the selected index from 0 to 6. Compare the index, the term value and the number of terms counted from the start

At index 4, how many terms have been counted, including index 0?

Three different quantities

An index labels a position. The term is the value at that position. A count of terms also includes the starting value

1. 1Stated convention These questions start at index 0. Other problems can use a different convention, so read the labels
2. 2Position Index 3 is the fourth position when counting from zero
3. 3Applications From index 0 to index 3 takes three updates, not four

Values beginning at index 0

\(\displaystyle -4,2,8,14,20\)

The list begins at t₀: −4, 2, 8, 14, 20. What is t₃?

Zero-indexed values

\(\displaystyle -4,2,8,14,20\)

In that same zero-indexed list, what index n has tₙ = 20?

For a list beginning at index zero, t₃ means:

Known and requested indices

\(\displaystyle 2,5\)

You already know t₂. How many updates are needed to reach t₅?

Read a later window using its labels

A displayed list need not begin at the initial term. If it begins at t₄, the next displayed value is t₅, not t₁

1. 1Use the given index Do not restart the subscripts merely because the display starts on a new line
2. 2Repeated values A value can occur at several indices. A value-to-index question needs enough information to identify the requested position

The zero-indexed list is 6, 9, 6, 9. At which displayed indices does the value 6 occur?

Later indexed terms

\(\displaystyle t_4=13,\quad t_5=18,\quad t_6=23\)

The labelled terms show a later window. What is t₅?

Can a term value be negative while its index is non-negative?

First and last indices

\(\displaystyle 0,6\)

A list includes t₀ through t₆. How many terms are listed?

In the table, why does t₂ = 2 not make the index and value the same concept?

Check what each blank asks for

A blank labelled tₖ asks for a value. A blank asking for n such that tₙ equals a given value asks for an index

1. 1Value lookup Find the row or position with the requested index, then read its value
2. 2Index lookup Find the given value first, then read its index. Check whether the value occurs more than once