SOLUTION: Please check the document for the question:
https://docs.google.com/document/d/1Cl3HrcoR6jibNzxfDTIilS3imSplLY8nQUU0OpU9vLA/edit?usp=sharing
Algebra.Com
Question 1185343: Please check the document for the question:
https://docs.google.com/document/d/1Cl3HrcoR6jibNzxfDTIilS3imSplLY8nQUU0OpU9vLA/edit?usp=sharing
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this looks like an arithmetic sequence type problem.
in an arithmetic sequence An = A1 + (n-1) * d
if d = 4, then An = A1 + (n-1) * 4
A2 would be equal to A1 + 1 * 4 which is equal to A1 + 4.
if A1 is equal to 10, then A2 would be equal to 14.
A3 would be equal to 10 + 2 * 4 = 18 which is also equal to A2 + 4
A4 would be equal to 10 + 3 * 4 = 22 which is also equal to A3 + 4
what this is saying is that An+1 is always equal to An + 4.
A20 would be equal to 10 + 19 * 4 = 10 + 76 = 86
the sum of an arithmetic sequence is equal to n/2 * (A1 + An).
since An = A1 + (n-1) * d, this formula can also be expressed as:
sum = n/2 * (A1 + A1 + (n-1) * d).
this becomes sum = n/2 * (2 * A1 + (n-1) * d).
either way, you'll get the sum.
if sum = n/2 * (A1 + An), you first have to find An.
when n = 20 and A1 = 10 and d = 4, A20 = 10 + 19 * 4 = 10 + 76 = 86.
sum is then equal to 20/2 * 10 + 86) = 10 * 96 = 960.
if sum = n/2 * (2 * A1 + (n-1) * d), then:
sum = 20/2 * (2 * 10 + 19 * 4) which becomes equal to 10 * (20 + 76) which is equal to 10 * 96 which is equal to 960.
the two formulas get you the same answer.
if you simply did the sum manually, you would get:
A1 = 10
A2 = 14
A3 = 18
A4 = 22
A5 = 26
A6 = 30
A7 = 34
A8 = 38
A9 = 42
A10 = 46
A11 = 50
A12 = 54
A13 = 58
A14 = 62
A15 = 66
A16 = 70
A17 = 74
A18 = 78
A19 = 82
A20 = 86
add those up and you get 960.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The definition
means each term is 4 more than the preceding term.
You are given u(1)=10, so the sequence is
10, 14, 18, 22, ...
The problem asks for the sum of the first 20 terms.
-----------------------------------------------------------------
With a common difference of 4 between successive terms, the sequence is arithmetic.
The sum of any set of numbers is the number of numbers, multiplied by the average of the numbers.
In an arithmetic sequence, because of the common difference between terms, the average of all the terms is the average of the first and last terms.
The last (20th) term is the first term 10, plus the common difference 19 times: u(20)=10+19(4)=86
So the sum of the first 20 terms in this sequence is the number of terms (20), multiplied by the average of the first and last terms ((10+86)/2=48).
ANSWER: 20*48 = 960
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