Answer:
the value of the 89th term is 36
Step-by-step explanation:
Given : [tex]A_{n} =\frac{20}{3} +\frac{1}{3} (n-1)[/tex]
To Find : 89th term
Solution :
The general explicit rule for an arithmetic sequence is
[tex]A_{n} = A_{1} +D(n-1)[/tex]
[tex]A_{1}[/tex] is the first term of sequence .
D is the common difference
so, in given sequence :
[tex]A_{1}= \frac{20}{3}[/tex]
[tex]D= \frac{1}{3}[/tex]
n = 89
so, to find 89th term
using given explicit formula :
[tex]A_{n} =\frac{20}{3} +\frac{1}{3} (n-1)[/tex]
put n = 89
⇒[tex]A_{89} =\frac{20}{3} +\frac{1}{3} (89-1)[/tex]
⇒[tex]A_{89} =\frac{20}{3} +\frac{1}{3} (88)[/tex]
⇒[tex]A_{89} =\frac{20}{3} +\frac{88}{3} [/tex]
⇒[tex]A_{89} =\frac{108}{3} [/tex]
⇒[tex]A_{n} = 36[/tex]
Thus, the value of the 89th term is 36
In the sequence and series, the value of the 89th term is 36.
A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after. A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.
Given
[tex]\rm A_n = \dfrac{20}{3} + \dfrac{1}{3}(n-1)[/tex]
To find
The value of the 89th term.
We know the standard equation is
[tex]\rm A_n = A_1 + D(n-1)[/tex]
On comparing
[tex]\rm A_1 = \dfrac{20}{3}[/tex], and D = 1/3
The 89th term will be for n = 89.
[tex]\rm A_n = \dfrac{20}{3} + \dfrac{1}{3}(n-1)\\\\\rm A_n = \dfrac{20}{3} + \dfrac{1}{3}(89-1)\\\\\rm A_n = \dfrac{20}{3} + \dfrac{1}{3}(88)\\\\\rm A_n = \dfrac{20}{3} + \dfrac{88}{3}\\\\\rm A_n = \dfrac{20 + 88 }{3} \\\\\rm A_n = \dfrac{108}{3} \\\\\rm A_n = 36[/tex]
Thus, the 89th term is 36.
More about the sequence and the series link is given below.
https://brainly.com/question/8195467
