|
Question 1047092: hi I am learning pre-calculus 11 and am stuck on this question thank you!
Q. Determine the sum, Sn, for each arithmetic sequence described.
a) T1=7, Tn=79, n=8
they do not tell me what D is, so I am confused.. :)
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! these are the formulas for an arithmetic sequence that i know.
http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm
they should be the same as your formulas, except they use a rather than T and d rather than D.
converting their formulas to your nomenclature, i get:
Tn = T1 + (n-1) * D
Sn = n * (T1 + Tn) / 2
from the formulas and from what you are given, you don't need to find D, but i'll show you how to find it anyway after solving the problem.
you are given:
a) T1=7, Tn=79, n=8
the formula for the sum of an arithmetic sequence is:
Sn = n * (T1 + Tn) / 2
you have what you need.
replace T1 with 7 and Tn with 79 and n with 8 and you have:
S8 = 8 * (7 + 79) / 2
solve for S8 to get S8 = 344
you didn't need D if you used the Sn formula.
you could solve for D as follows:
the formula for Tn is:
Tn = T1 + (n-1) * D
replace Tn with 79 and T1 with 7 and n with 8 and you get:
79 = 7 + (8-1) * D
simplify to get:
79 = 7 + 7 * D
subtract 7 from both sides of the equation to get:
72 = 7 * D
solve for D to get:
D = 72/7.
your formula of Tn = T1 + (n-1) * D becomes T8 = 7 + 7 * 72/7
solve for T8 to get T8 = 79.
value of D looks good.
you can also calculate each term from 1 to 8 and then add them up to see if the formula work as advertised.
you get:
T1 = 7 = 49/7
T2 = 7 + 1 * 72/7 = 121/7
T3 = 7 + 2 * 72/7 = 193/7
T4 = 7 + 3 * 72/7 = 265/7
T5 = 7 + 4 * 72/7 = 337/7
T6 = 7 + 5 * 72/7 = 409/7
T7 = 7 + 6 * 72/7 = 481/7
T8 = 7 + 7 * 72/7 = 553/7
add them up and you get a total of 2408/7 which is equal to 344.
the formulas look good.
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
hi I am learning pre-calculus 11 and am stuck on this question thank you!
Q. Determine the sum, Sn, for each arithmetic sequence described.
a) T1=7, Tn=79, n=8
they do not tell me what D is, so I am confused.. :)
~~~~~~~~~~~~~~~~~~~~
There are two formulas for the sum of an arithmetic progression.
The first formula is
 =  =  .
It really requires to know the "d", the common difference.
But there is another formula for the sum of an arithmetic progression:
=  .
for which to know  ,  and n is enough.
So, use this second formula, and you get
 =  =  = 344.
For arithmetic progressions, see the lessons
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
- Chocolate bars and arithmetic progressions
- Mathematical induction and arithmetic progressions
- One characteristic property of arithmetic progressions
- Mathematical induction for sequences other than arithmetic or geometric
- Proving inequalities by the method of Mathematical Induction
- Solved problems on arithmetic progressions
OVERVIEW of my lessons on arithmetic progressions with short annotations is in the lesson OVERVIEW of lessons on arithmetic progressions.
|
|
|
| |
