Question

Write a function rule for the following arithmetic sequence and use it to find the 224th term. Show your work.

Answer 1

Answer:

Function rule for the arithmetic sequence is; $a_n = a+(n-1)d$

The 224th term of the arithmetic sequence  is: 671

Step-by-step explanation:

Arithmetic sequence: A sequence of number which increases or decreases by a constant amount each term.

Formula for nth term of arithmetic sequence is:

$a_n = a+(n-1)d$

where a is the first term in the sequence, d is the common difference and n is the number of terms;

Given an arithmetic sequence:

2, 5 , 8, 11, ......

First term(a) = 2

Common difference(d) = 3 (Because the difference between the two consecutive terms is 3) i,e

5-2 = 3

8-5 = 3

11 -8 =3 ans so on,....

To find the 224th term;

we have,

a = 2 , d = 3 and n = 224

Using formula for nth arithmetic sequence;

$a_{224} = 2+(224-1)(3)$

$a_{224} = 2+(223)(3)$

$a_{224} = 2+669$ =671

therefore, the 224th term for the given arithmetic sequence is, 671

Answer 2

Answer:

671  is the 224th term of the given series

Step-by-step explanation:

The given sequence is

2,5,8,11....

First term that is 2

common difference that is 3

we have to find 224th term

That is n =224

using $a_n=a+(n-1)d$

$a_{224}=2+(224-1)3$

On solving the above equation we get

$a_{224}=671$

Hence, 224th term of the given series is 671