Calculate terms of a recurrence sequence on one line

Find successive terms of a recurrence and keep track of their term numbers using a two-statement CALC loop.

6 langkah

Artikel ini belum tersedia dalam bahasa Indonesia. Versi lengkap bahasa Inggris ditampilkan.

You know the first term and a rule for finding the next one. How can you calculate several terms without retyping the rule? For this example, find $u_{2}$ through $u_{5}$ :

u_{1} = 1, u_{n + 1} = 2 u_{n} + 1.

Use $x$ to count the term number $n$ and $a$ to hold the current term $u_{n}$ . Enter two statements on one line:

x = x + 1 : a = 2 a + 1

The first statement increases the counter; the second doubles the current term and adds one. Start both $x$ and $a$ at $1$ .

Enter the recurrence and calculate the terms

Below each step is the screen you should see after pressing.

Next to each step is the screen you should see after pressing.

Step 1

Type $x = x + 1 : a = 2 a + 1$ . Use the keys shown for the equals sign (the equals key that runs a calculation does not type one) and for the colon, which separates the two statements. The completed line has no result yet.

Press:
Step 2

Start CALC with the key shown. The $x =$ prompt opens.

Press:
Step 3

Enter $1$ for $x$ and press the equals key, then enter $1$ for $a$ . The $a =$ prompt now shows $1$ ; do not press the equals key yet.

Press:
Step 4

Press the equals key twice. The first press shows $2 \to x$ ; the second shows $3 \to a$ . You have found $u_{2} = 3$ .

Press:
Step 5

Press the equals key four times, keeping the values shown at the $x =$ and $a =$ prompts. You pass through $3 \to x$ and finish at $7 \to a$ , so $u_{3} = 7$ .

Press:
Step 6

Press the equals key eight more times to complete two more passes. Read $4 \to x$ , then $15 \to a$ for $u_{4}$ ; the final pass shows $5 \to x$ , then $31 \to a$ for $u_{5}$ .

Press:

Read and check the terms

Read the number sent to $a$ as the sequence term and the number sent to $x$ as its position:

n u_{n} 112337415531

For example, $31 \to a$ means $31$ has been stored in $a$ . Check the last term by hand: $2 \times 15 + 1 = 31$ .

After each completed pass, the next term takes four presses of the equals key: revisit $x =$ , revisit $a =$ , update $x$ , then update $a$ . Keep the prompted values to continue. The loop keeps cycling, so stop when you have the terms you need; AC leaves the loop and keeps the line.

For repetition without a counter, enter $1$ and press the equals key, then enter $\times 2 + 1$ to make $Ans \times 2 + 1$ and press the equals key repeatedly for $3, 7, 15, 31, \dots$ , one press per term.

If your result is different

You do not get sequence terms: the equals key on the typed line does not start the loop. Start CALC as in step 2, then enter both starting values.
The first pass shows $1 \to x$ and $1 \to a$ : a prompt keeps the value it shows when you press the equals key without typing, and a letter that was never set shows $0$ . At the prompts, type $1$ for $x$ and $1$ for $a$ to replace the shown values, then continue from step 4.
A new run starts from the previous terms: the loop keeps the last stored values of $x$ and $a$ . Enter both starting values again to restart the example; you can check and change a stored variable afterwards.

The fx-991EX screen showing x=x+1 : a=2a+1 and the fifth term, 31, stored in a.

Calculate recurrence terms on your fx-991EX calculator

Start with x = 1 and a = 1, then run the two-statement CALC loop to find the fifth term, 31.

Calculate the terms More guides

Enter the recurrence and calculate the terms

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Read and check the terms

If your result is different

Calculate recurrence terms on your fx-991EX calculator