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Write an expression to describe a rule of the sequence. Then find the 100th term in the sequence.

4, 9, 14, 19, 24, 29.....

A)4+5n;504

B)5n-1; 499

C5n; 500
D4n+5; 405

Verified Answer :

A) 4+5n;504  Would be ur answer!!

Hope i helped:P 

Answer:

Option B is correct

\(a_n = 5n-1\); 499

Step-by-step explanation:

The nth term for the arithmetic sequence is given by:

\(a_n = a_1+(n-1)d\)         ....[1]

where,

\(a_1\) is the first term

d is the common difference of two successive terms

n is the number of terms.

As per the statement:

4, 9, 14, 19, 24, 29.....

This is a arithmetic sequence.

Here, \(a_1=4\) and d =5

Since,

9-4 = 5,

14-9 =5,

19-14 = 5 and son on....

Substitute the given values in [1] we have;

\(a_n = 4+(n-1)5\)

⇒\(a_n = 4+5n-5 = 5n-1\)

⇒\(a_n = 5n-1\)

We have to find the  100th term in the given sequence.

For n= 100

\(a_{100} = 5(100)-1=500-1 =499\)

⇒\(a_{100} = 499\)

Therefore,  an expression to describe a rule of the sequence is, \(a_n = 5n-1\) and the 100th term in the sequence is 499

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