Right an expression to describe a rule for the sequence then find the 100th term in the sequence 4, 9, 14, 19, 24, 29,..
A. 4 + 5 ;504
B. 5 and - 1 ; 499
C. 5 n; 500
D. 4n + 5; 405
The common difference between consecutive terms in the sequence is 5, so the rule can be described as adding 5 to the previous term to get the next term.
Using this rule, we can find the 100th term as follows:
First term = 4
Second term = 4 + 5 = 9
Third term = 9 + 5 = 14
Fourth term = 14 + 5 = 19
And so on.
The 100th term would be:
99th term = 4 + (99-1)5 = 4 + 490 = 494
100th term = 494 + 5 = 499
Therefore, the expression that correctly describes the rule is D) 4n + 5, and the 100th term in the sequence is 499.