arithmatic sequences

[yfelix45]

Hello,
can you verify if I have done this right?


Find t^n for the following arithmatic sequence 100, 92, 84.... Then use the t^n to find t ^20.


What I have done:

a = 100 d = 92 - 100 = -8

t^n = 100 + (20 - 1 )(- 8 )
= 100 + (19) (- 8)
= 100 - 152
= -52.
Thanks

yfelix45

 

[Mrspi]

Hello,
can you verify if I have done this right?


Find t^n for the following arithmatic sequence 100, 92, 84.... Then use the t^n to find t ^20.


What I have done:

a = 100 d = 92 - 100 = -8

t^n = 100 + (20 - 1 )(- 8 )
= 100 + (19) (- 8)
= 100 - 152
= -52.
Thanks

yfelix45

It looks like you are asked to find the expression for the general term t_n.....

for an arithmetic sequence,

t_n = a + (n - 1)*d

You have correctly determined, using the given terms, that n = -8. And, from the given terms, we can see that the intial term "a" is 100.

So......for this particular sequence,

t_n = 100 + (n - 1)*(-8), or
t_n = 100 - 8n + 8, or
t_n = 108 - 8n

THAT is the formula for the general term.


And you can find the 20th term of that sequence by substituting 20 for n....
t₂₀ = 108 - 8(20)

 

[yfelix45]

thank you

hello Mrspi,

Thank you for correcting my mistake. When I first attempted the question, that formula was the first I tried but I did it wrong.

Thanks again

yfelix45