FIND THE DIFFERENCE
What is the exact common difference, d, for the sequence 20, 18, 16, 14?
-2
What is the simplified expression, in terms of n, for the sequence 4, 7, 10, 13?
3n + 1
If the nth~term of a sequence is defined as 3n + 1, what is the value of the 50th term?
151
Given that the ith term of a sequence is 3n + 1, at what position n is the value 61?
20 (61 = 3n + 1 -> 60 = 3n -> n = 20)
True or False: In any arithmetic sequence, the common difference d is found by subtracting the next term from the previous term.
False. It is the Next Term minus the Previous Term.
If an arithmetic sequence starts at 7 and has a common difference of 13, what is the value of the 4th term?
46 (7, 20, 33, 46)
If the first term a = -5 and the common difference d = 4, what is the simplified nth~term expression?
4n - 9
The nth~term of a sequence is 10n - 2. What is the 100th term?
998 (10(100) - 2)
Given that the Kth term of the sequence 3n + 1 is 91, what is K?
30 (91 = 3K + 1 -> 90 = 3K -> K = 30)
If you add the 1st term and the 3rd term of any arithmetic sequence together, and then divide that sum by 2, what specific term will you always get?
The 2nd term (The average of the 1st and 3rd terms is always the middle term).
A sequence has a 3rd term of 15 and a 4th term of 11. What is the value of the 1st term?
23 (The sequence goes backward: 23, 19, 15, 11)
What is the nth~term expression for a sequence where every term is identical, such as 8, 8, 8, 8?
8 (or 0n + 8)
For the even number sequence starting 2, 4, 6, 8..., what is the 500th term?
1000 (2 x 500)
A sequence is defined by the formula 5n. Which position number holds the value 225?
45th position (225 / 5 = 45)
Sequence A has the formula 2n. Sequence B has the formula 2n + 5. What is the constant difference between the corresponding terms of Sequence B and Sequence A?
5 (Every term in Sequence B is exactly 5 more than Sequence A).
The 10th term of a sequence is 50 and the 11th term is 53. Without using a formula, what is the 12th term?
56 (Difference is +3, so 53 + 3 = 56)
An arithmetic sequence decreases by 5 each time and starts at 100. What is the simplified nth~term expression?
105 - 5n (100 + (n-1)(-5) = 100 - 5n + 5)
An arithmetic sequence has the formula nth~term = 1 - 2n. What is the 25th term?
-49 (1 - 2(25) = 1 - 50)
A sequence begins 100, 90, 80, 70... At what exact position n does the sequence hit 0?
11th position (Formula is 110 - 10n. 0 = 110 - 10n -> 10n = 110 -> n = 11)
An arithmetic sequence has a positive first term but a negative common difference. Conceptually, will this sequence eventually contain negative numbers?
Yes (Because subtracting a constant number endlessly will eventually cross zero into the negatives).
An arithmetic sequence has a 1st term of 5 and a 3rd term of 17. What is the common difference?
+6 (Gap of two steps between 1st and 3rd term is 12, so 12 / 2 = 6)
If the nth~term of a sequence is -3n + 12, what is the very first term of the sequence?
9
If the 100th term of a sequence is 200 and the common difference is 2, what is the 99th term?
198 (Just subtract the common difference once: 200 - 2)
The nth~term formula is 4n - 3. If a term in this sequence has the value 37, what is the value of the term immediately preceding it?
33 (First find n: 37 = 4n - 3 -> 40 = 4n -> n = 10. The 9th term is 4(9) - 3 = 33, or simply subtract the common difference of 4 from 37).
Two arithmetic sequences share the exact same common difference, but Sequence Y starts with a number 10 higher than Sequence X. If the 5th term of Sequence X is 30, what is the 5th term of Sequence Y?
40 (Because the sequences advance at the exact same rate, Sequence Y will always be exactly 10 higher than Sequence X at any given position).