Question

how would I Identify the 20th term of the arithmetic sequence 3,7,11

Answer 1

what's the common difference, "d", you think?

that is, how much is being "added" to one term to get the next one?

Answer 2

it's 4 @jdoe0001

Answer 3

so d = 4 then \(\bf a_{\color{brown}{ n}}=a_1+({\color{brown}{ n}}-1){\color{blue}{ d}}
\\ \quad \\
a_1=\textit{1st term}\qquad thus\quad a_{\color{brown}{ n}}=5+({\color{brown}{ n}}-1){\color{blue}{ (4)}}
\\ \quad \\
20^{th}\ term\implies a_{\color{brown}{ 20}}=5+({\color{brown}{ 20}}-1){\color{blue}{ (4)}}\)

Answer 4

Lost me there

Answer 5

https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcR3BsPEWtbQQTC0wbeA5rmnmrIRZUq6-J84ayK5HjquGjHPA4Fv <---

Answer 6

@jdoe0001 I'm still confused

Answer 7

http://www.youtube.com/watch?v=lj_X9JVSF8k <--- arithmetic sequences, which is what this one is

Answer 8

@jdoe0001 its 79

Answer 9

got it thanks i understand

Answer 10

ohh yeah.. the 1st term was 3... yeap

I had 5 as typo \(\bf a_{\color{brown}{ n}}=a_1+({\color{brown}{ n}}-1){\color{blue}{ d}}
\\ \quad \\
a_1=\textit{1st term}\qquad thus\quad a_{\color{brown}{ n}}=3+({\color{brown}{ n}}-1){\color{blue}{ (4)}}
\\ \quad \\
20^{th}\ term\implies a_{\color{brown}{ 20}}=3+({\color{brown}{ 20}}-1){\color{blue}{ (4)}}\)

Answer 11

but did i do it right @jdoe0001

Answer 12

yeap \(\bf a_{\color{brown}{ n}}=a_1+({\color{brown}{ n}}-1){\color{blue}{ d}}
\\ \quad \\
a_1=\textit{1st term}\qquad thus\quad a_{\color{brown}{ n}}=3+({\color{brown}{ n}}-1){\color{blue}{ (4)}}
\\ \quad \\
20^{th}\ term\implies a_{\color{brown}{ 20}}=3+({\color{brown}{ 20}}-1){\color{blue}{ (4)}}\implies a_{\color{brown}{ 20}}=3+19\cdot 4
\\ \quad \\
a_{\color{brown}{ 20}}=3+76\to 79\)