SOLUTION: How to find the sum of the first 10 terms of each arithmetic sequence? 1. a(sub1) = 11 and a(sub10) = 38 2. a (sub1) = 10 and a(sub10) = 55

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: How to find the sum of the first 10 terms of each arithmetic sequence? 1. a(sub1) = 11 and a(sub10) = 38 2. a (sub1) = 10 and a(sub10) = 55      Log On


   

Question 1086131: How to find the sum of the first 10 terms of each arithmetic sequence?
1. a(sub1) = 11 and a(sub10) = 38
2. a (sub1) = 10 and a(sub10) = 55
Found 3 solutions by Fombitz, MathTherapy, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do one, you do the other the same way.
a%5B10%5D=a%5B1%5D%2B%2810-1%29d
38=11%2B9d
9d=27
d=3
So,
a%5B2%5D=a%5B1%5D%2B%282-1%29d=11%2B%281%293=11%2B3=14
a%5B3%5D=a%5B1%5D%2B%283-1%29d=11%2B%282%293=11%2B6=17
a%5B4%5D=a%5B1%5D%2B%284-1%29d=11%2B%283%293=11%2B9=20
Continue this until you get all 10 terms.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
How to find the sum of the first 10 terms of each arithmetic sequence?
1. a(sub1) = 11 and a(sub10) = 38
2. a (sub1) = 10 and a(sub10) = 55
Use the formula for the sum of an AP: S%5Bn%5D+=+%28n%2F2%29%28a%5B1%5D+%2B+a%5Bn%5D%29, where:

S%5Bn%5D = Sum of the 1st 10 terms (S%5B10%5D, in this case)

n  = Number of terms (10, in this case)

a%5B1%5D = 1st term (11, in this case)

a%5Bn%5D = Value of last term (38, in this case)

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
How to find the sum of the first 10 terms of each arithmetic sequence?
1. a(sub1) = 11 and a(sub10) = 38
2. a (sub1) = 10 and a(sub10) = 55
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  Use the formula for the sum of an arithmetic progression

    S%5Bn%5D = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An:   S%5B10%5D%7D+=+%7B%7B%7B%28%28a%5B1%5D%2Ba%5B10%5D%29%2F2%29%2A10 = %28%2811%2B38%29%2F2%29%2A10 = %2849%2F2%29%2A10 = 24.5*10 = 245.

    You do not need to calculate the common difference in this case.



2.  Do THE SAME:

    S%5Bn%5D = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An:   S%5B10%5D = %28%28a%5B1%5D%2Ba%5B10%5D%29%2F2%29%2A10 = %28%2810%2B55%29%2F2%29%2A10 = %2865%2F2%29%2A10 = 32.5*10 = 325.

    Again, you do not need to calculate the common difference in this case.


See introductory lessons on arithmetic progressions in this site
    - Arithmetic progressions (*)
    - The proofs of the formulas for arithmetic progressions (*)
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions

The lessons marked (*) contain the formulas to sum arithmetic progression: read them very attentively.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".