Use the sequence ... an=1/4n+8 for Part A, Part B, and Part C.

Question

Part A: Find the eighth term in the sequence. Show your work.

Part B: Tessa says that the fourth term in the sequence is 7. Is Tessa correct? 

Part C: Explain why or why not. Show your work to support your answer. 

Answer 1

an = 1/(4n+8) or an = (1/4n) + 8? the problem is ambiguous

try the 1st interpretation

a1 = 1/12

a2 = 1/16

a3 = 1/20

a4 = 1/24 which doesn't = 7

...

a8 =1/40

You might want the 2nd interpretation

a1 =1/4 + 8 = 8.25

a2 =1/8 + 8 = 8 1/8

...

a4 = 1/16 + 8 = 8 1/16 which also doesn't = 7

a8 = 8 1/32

no term in this sequence would ever =7

Or maybe you meant an=(1/4)n + 8

then a4 = (1/4)4+ 8 = 9 which also doesn't equal 7

a8 = 10

Or maybe you meant an = (1/4)(n+8)?

then a4 = (1/4)12 = 3 which also doesn't equal 7

a8 = 4

a12 =5

a16=6

but the 20th term in this sequence would = 7, a20 = (1/4)(20+8) = 28/4 = 7

seems like the only way to get 7 for any term in any related sequence, however you interpret the problem.

Maybe there's a typo and minus sign missing

an =-(1/4)n + 8

then

a4 =-(1/4)4 + 8 = -1+8 = 7

and a8 = -(1/4)(8) + 8 = 6