Difference between revisions of "2002 AMC 10P Problems/Problem 5"

Revision as of 17:40, 14 July 2024

Let $(a_n)_{n \geq 1}$ be a sequence such that $a_1 = 1$ and $3a_{n+1} - 3a_n = 1$ for all $n \geq 1.$ Find $a_{2002}.$

$\text{(A) }666 \qquad \text{(B) }667 \qquad \text{(C) }668 \qquad \text{(D) }669 \qquad \text{(E) }670$

2002 AMC 10P (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

@@ Line 1: / Line 1: @@
+== Problem 5 ==
+Let <math>(a_n)_{n \geq 1}</math> be a sequence such that <math>a_1 = 1</math> and <math>3a_{n+1} - 3a_n = 1</math> for all <math>n \geq 1.</math> Find <math>a_{2002}.</math>
+<math>
+\text{(A) }666
+\qquad
+\text{(B) }667
+\qquad
+\text{(C) }668
+\qquad
+\text{(D) }669
+\qquad
+\text{(E) }670
+</math>
 == Solution 1==