Question

Find the 137th odd number.

Answer 1

ok, so IDK why my answer was deleted even though it was correct but here goes. it would be nice if you comment to ask me to fix what's wrong instead of just deleting the answer

1st odd number is 1

2nd odd number is 3

3rd odd number is 5

it seems like the mod did not like my method so we will try to find an aritmetic sequence since each term increases by the same amount

the formula for an aritmetic sequence is $a_n=a_1+d(n-1)$ where

$a_n$ is the nth term (you can also write f(n) if you need a function)

$a_1$ is the first term

d is the common differnce or how much each term increases by ($d=a_n-a_{n-1}$)

n is the counter to tell us what term we are on

so

1st term is 1 so $a_1=1$

each term increases by 5-3=2 and 3-1=2, by 2, so d=2

therefore, $a_n=1+2(n-1)$

the 137th term would be $a_{137}=1+2(137-1)$

$a_{137}=1+2(136)$

$a_{137}=1+272$

$a_{137}=273$

the 137th odd number is 273

Answer 2

The first odd number is 1. The next is 2 more than the previous one.

It's an arithmetic sequence.

The general term of an arithmetic sequence:

$a_n=a_1+(n-1)d$

a_n - n-th term

a_1 - first term

d - common difference.

We have

$a_1=1,\ d=2,\ n=137$

Substitute:

$a_{137}=1+(137-1)(2)=1+(136)(2)=1+272=273$

Answer: 137th odd number is equal 273.