Question

find the nth term of 5/3, 7/3 ,3 ,11/3 ,13/3 ,5...​

Answer 1

Answer:

2n/3 + 1

Step-by-step explanation:

since the series is an arithmetic progression,

common difference = 7/3 - 5/3 = 2/3

first term = 5/3

so, using formula

T_n = a + (n-1)d

= 5/3 +(n-1)2/3

= 2n/3 + 1

Answer 2

Answer:    

nth term of the number series = $1 + \frac{2n}{3}$            

Given problem:    

Find the nth term of 5/3, 7/3 ,3 ,11/3 ,13/3 ,5...​                          

Step-by-step explanation:  

Given number sequence =  5/3, 7/3 ,3 ,11/3 ,13/3 ,5...​  

here we need to find nth term of the given series

if we observe difference between every 2 terms is same

therefore we can conclude that the given number series is in AP

Here 1st term  a = 5/3

and common difference d = 2/3  

nth term in a AP,  T$_{n}$ = a+(n-1)d  

                                  =  $\frac{5}{3} +(n-1)(\frac{2}{3} )$  

                                  =  $\frac{5}{3} + (\frac{2n-2}{3} )$    

                                  =  $\frac{5 +2n-2}{3}$  

                                  =   $\frac{3 +2n}{3}$  

                                  =  $\frac{3}{3} + \frac{2n}{3}$  

                                  =  $1 + \frac{2n}{3}$