if u_n = 2 + 5n , find
a. a recursive definition
b. the common difference
c. n such that u_n = 102.
i hate asking for homework help on here, but i actually have no clue what to do. ive googled, watched videos, and listened to my teacher but its just not helping... i know how to find explicit and recursive formulas, from the a_1 and other simple stuff, im just not sure how we're supposed to figure it out from where they've simplified it to... thank you so much in advance!
ps, if you only want to answer a. i can probably figure it out from there, if you don't like giving out answers! i just need to be walked through it a little :)
a. a recursive definition
b. the common difference
c. n such that u_n = 102.
i hate asking for homework help on here, but i actually have no clue what to do. ive googled, watched videos, and listened to my teacher but its just not helping... i know how to find explicit and recursive formulas, from the a_1 and other simple stuff, im just not sure how we're supposed to figure it out from where they've simplified it to... thank you so much in advance!
ps, if you only want to answer a. i can probably figure it out from there, if you don't like giving out answers! i just need to be walked through it a little :)
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I would hate to tell you what you would find if you googled recursive defintion. I can probably do this, but I'm not sure I can do it in such a way that it answers what you've been told. It is no wonder to me that you are having problems. The definitions I've read lead me to believe that people use language as though it was a battle ax instead of a rapier. Clarity clarity. We seek clarity.
The common difference is found by considering u_n and u_n+1 Since u_n+1 is presumed larger put it first.
u_n+1 - u_n = (2 + 5(n + 1)) - (2 + 5n) remove the brackets.
u_n+1 - u_n = (2 + 5(n + 1)) - (2 + 5n)
d = u_n+1 - u_n = (2 + 5n + 5 - 2 - 5n)
d = 5
To find what u_102 is you need the first term
u_1 = 2+5(1) = 7
102 = u_1 + (n-1)*d
102 = 7 + (n - 1)*5 Subtract 7
95 = 5*(n - 1) divide by 5
19 = n - 1 Add 1
n = 20
I suppose the recursive formula should be
u_n+1 = u_n + 5. That's my best guess (and I program as a hobby).
The common difference is found by considering u_n and u_n+1 Since u_n+1 is presumed larger put it first.
u_n+1 - u_n = (2 + 5(n + 1)) - (2 + 5n) remove the brackets.
u_n+1 - u_n = (2 + 5(n + 1)) - (2 + 5n)
d = u_n+1 - u_n = (2 + 5n + 5 - 2 - 5n)
d = 5
To find what u_102 is you need the first term
u_1 = 2+5(1) = 7
102 = u_1 + (n-1)*d
102 = 7 + (n - 1)*5 Subtract 7
95 = 5*(n - 1) divide by 5
19 = n - 1 Add 1
n = 20
I suppose the recursive formula should be
u_n+1 = u_n + 5. That's my best guess (and I program as a hobby).
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It turns out that (b) and (c) are easier than (a).
List out the first few terms of the sequence to get a feel of it by plugging in n = 1, 2, 3, etc. This gives us:
7, 12, 17, 22, ...
(b) Clearly, this is an arithmetic sequence with common difference d = 5.
(c) Solve for n:
u_n = 2 + 5n
102 = 2 + 5n
100 = 5n
n = 20
(a) Okay, the harder part. Notice that each term is 5 more than the previous term. Thus, we have:
u_1 = 7 and u_n = u_(n - 1) + 5 for n = 2, 3, ...
List out the first few terms of the sequence to get a feel of it by plugging in n = 1, 2, 3, etc. This gives us:
7, 12, 17, 22, ...
(b) Clearly, this is an arithmetic sequence with common difference d = 5.
(c) Solve for n:
u_n = 2 + 5n
102 = 2 + 5n
100 = 5n
n = 20
(a) Okay, the harder part. Notice that each term is 5 more than the previous term. Thus, we have:
u_1 = 7 and u_n = u_(n - 1) + 5 for n = 2, 3, ...
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I'm confused