What are the first three terms in the sequence for $-2 n+5$?
A. $-3,-1,1$
C. $3,1,-1$
B. $-2,1,4$
D. $2,-1,-4$
Answer (1)
Substitute n = 1 into − 2 n + 5 to find the first term: − 2 ( 1 ) + 5 = 3 .
Substitute n = 2 into − 2 n + 5 to find the second term: − 2 ( 2 ) + 5 = 1 .
Substitute n = 3 into − 2 n + 5 to find the third term: − 2 ( 3 ) + 5 = − 1 .
The first three terms are 3 , 1 , − 1 , so the answer is 3 , 1 , − 1 .
Explanation
Understanding the Problem We are given the sequence defined by the formula − 2 n + 5 , and we need to find the first three terms of this sequence. This means we need to substitute n = 1 , n = 2 , and n = 3 into the formula and calculate the resulting values.
Finding the First Term To find the first term, we substitute n = 1 into the formula: − 2 ( 1 ) + 5 = − 2 + 5 = 3
Finding the Second Term To find the second term, we substitute n = 2 into the formula: − 2 ( 2 ) + 5 = − 4 + 5 = 1
Finding the Third Term To find the third term, we substitute n = 3 into the formula: − 2 ( 3 ) + 5 = − 6 + 5 = − 1
Listing the Terms and Choosing the Correct Option Therefore, the first three terms of the sequence are 3 , 1 , − 1 . Comparing this to the given options, we see that it matches option C.
Examples
Sequences are used in computer science for analyzing algorithms, in finance for modeling stock prices, and in physics for describing the motion of objects. For example, the sequence − 2 n + 5 could represent the remaining battery life of a device after n hours of usage, starting with 5 units of battery life and decreasing by 2 units each hour. Understanding sequences helps in predicting future values and making informed decisions in various fields.
