Given the sequence 8, 11, 14, 17,..., which of the following represents a formulas that will generate it? f(n) = 3n + 8
f(n) = 3n + 5
f(n) = 8n + 3
f(n) = 8n + 8

f(n) = 3n + 5

Step-by-step explanation:

Given sequence  8, 11, 14, 17,...

it is an arithmetical progression (AP)series

in AP series

nth term is given by

nth term = a + (n-1)d

where a is first term

d is the common difference

common difference  is calculated as = nth term - (n-1)th term

lets take nth term and (n-1)th term as 2nd term and 1st term

d = 11-8 = 3

Thus, common difference is 3

first term is 8

nth term is given by

nth term = a + (n-1)d

               = 8+(n-1)3

              = 8 + 3n -3

              = 5 + 3n

The formula that will generate the sequence 8, 11, 14, 17,...,

is option f(n) = 3n + 5

A quick way to find this is take any value of the series and determine its term number and put value of term in the option . The option which gives the same value as in the sequence is the correct choice

Example

8 is the 1st term

so in place of n put 1 in all the option. The option which will give value as 8 is correct answer.