Question

What is the formula for the nth term of the given sequence 1,9,17...

Answer 1

1,9,17,25,33,41,49,57,65,73 it’s always going up by 8 Example: 1+8= 9 9+8=17

Answer 2

t(n) = 8n - 7

Explanation:

Formula for Arithmetic Sequence: t(n) = (CD)n + t(0)

• t(n) is the value of the term
• CD is a Common Difference, more about that soon
• n is the term number
• t(0) is the 0th term (the first value of all sequences is the first term)

Solve: Common Difference

Just like how you would solve for slope, you would solve for the CD

• CD = (term value - previous term value)/(term # - previous term #)
• CD = (9 - 1)/(2 - 1)
• CD = 8/1
• CD = 8

Now, we have the equation : t(n) = 8n + t(0)

Now we have to solve for t(0), the y-intercept of the 0th term

Solve: t(0)

Do this the same way you would solve for b in y = mx + b

• t(n) = (CD)n + t(0)
• 1 = 8(1) + t(0) <= Input output for t(n), and term number for n
• 1 = 8 + t(0)
• -7 = t(0)

Our final equation is
`\boxed{\text{t(n) = 8n - 7}}`

-Chetan K