Question

The explicit rule for an arithmetic sequence is An=20/3 / 1/3 (n-1)

Answer 1

Answer:

the value of the 89th term is 36

Step-by-step explanation:

Given : $A_{n} =\frac{20}{3} +\frac{1}{3} (n-1)$

To Find : 89th term

Solution :

The general  explicit rule for an arithmetic sequence  is

$A_{n} = A_{1} +D(n-1)$

$A_{1}$  is the first term of sequence .

D is the common difference

so, in given sequence :

$A_{1}= \frac{20}{3}$

$D= \frac{1}{3}$

n = 89

so, to find 89th term

using given explicit formula :

$A_{n} =\frac{20}{3} +\frac{1}{3} (n-1)$

put n = 89

⇒$A_{89} =\frac{20}{3} +\frac{1}{3} (89-1)$

⇒$A_{89} =\frac{20}{3} +\frac{1}{3} (88)$

⇒$A_{89} =\frac{20}{3} +\frac{88}{3}$

⇒$A_{89} =\frac{108}{3}$

⇒$A_{n} = 36$

Thus, the value of the 89th term is 36

Answer 2

We are to solve for the 89 term of the Arithmetic equation given below:
An = 20/3 + 1/3 (n-1)
Replacing n with 89, we have:
An = 20/3 + 1/3 (89-1)
An =20/3 + 1/3 (88)
An = 20/3 +88/3
An =108/3
An = 36

The 89th term is 36.