7. Four friends agree to save money for a graduation road trip. They decide that each of them will put $0.25 in the fund on the first day of May, $0.50 on the second day, $0.75 on the third day, and so on. At the end of May, there will be $_____ in their fund. (Hint: There are 31 days in May.)
7. Ans:
Since there are 4 friends,
A1 = $0.25 x 4 = $1.00
A2 = $0.50 x 4 = $2.00
A3 = $0.75 x 4 = 3.00
=> d = $3.00 – $2.00 = $2.00 – $1.00 = $1.00
d = $1.00
We r lookin’ 4 d sum of money in May, where sum, Sn, is given as;
Sn = (n/2) [2a1 + (n – 1)d]
Where;
n = nos of days in may = 31
d = $1.00
a = $1.00
S31 = (31/2) [2(1) + (31 – 1)1]
S31 = (31/2) [2 + 30(1)]
S31 = (31/2) [2 + 30] = (31/2) [32]
S31 = 31 x 16
S31 = 496
Ans = $496
2. Which of the following are arithmetic sequences?
Ans:
= 3, 6, 9, 12, 15, ….
Because 15 – 12 = 12 – 9 = 9 – 6 = 6 – 3 = 3 = d
3. Ans:
Yes,ust plug in the number 10:
A10 = 3(10) / (10 + 1)
A10 = 30 / 11
5. Didn’t understand d que!!
6. The sequence an = 8, 13, 18, 23, … is the same as the sequence a1 = 8, an = an-1 + 5.
Ans:
True
Because, when an = 23, an-1 = 18 => 23 = 18 + 5
When an = 18, an-1 = 13 => 18 = 13 + 5
9. Which of the numbers below could be terms in the sequence an = 3n + 16?
Ans:
46 => 46 – 16 = 30 = 3n where n = 10
48 => 48 – 16 = 32 nt = 3n
61 => 61 – 16 = 45 = 3n where n = 15
64 => 64 – 16 = 48 = 3n where n = 16
Ans = A, C, D [46, 61, 64]
10. Ans:
First find A1, A2, A3 in order to obtain the common difference, d;
An = 7n + 2
A1 = 7(1) + 2
A1 = 7 + 2 = 9
A2 = 7(2) + 2
A2 = 14 + 2 = 16
A3 = 7(3) + 2
A3 = 21 + 2 = 23
d = A3 – A2 = A2 – A1 = 23 – 16 = 16 – 9 = 7
Sn = (n/2) [2a1 + (n – 1)d]
S20 = (20/2) [2(9) + (20 – 1)7]
S20 = 10 [18 + (19)7]
S20 = 10 [18 + 133] = 10 [151]
S20 = 1510
Check the image given in the source for the working of the first question. I will explain it below:
1. ‘a’ is the first term of the sequence, ‘d’ is the difference between the first and second term, ‘n’ is the number of terms.
2. Note the formula. This is the formula used to find the sum of an arithmetic series.
3. Substitute the values of ‘a’, ‘d’ and ‘n’ in the formula and calculate the answer.
4. Multiply it by 4 because there are 4 guys.
Second Question: (Check the image for the working)
1. An arithmetic sequence is a sequence where the difference between each the terms are the same. You can only add or subtract the previous term to get to next term.
2. The second and third sequences are multiplying to get the next term, therefore they are not arithmetic series. In fact, they are geometric series.
3. The last sequence doesn’t have the same difference between all numbers so it is also not an arithmetic series.
4. The only arithmetic series/sequence is the first one.
Third Question:
Yes, just plug in the number 10.
Forth and Fifth:
I don’t know. Sorry.
Sixth Question: (Check image)
1. Put all the numbers in the formula.
2. If you get a whole number, then it can be a term of that sequence.
3. Therefore, the answer is A,C and D.
Last Question: (Check image, sorry about the mess)
1. Find ‘a’ and ‘d’.
2. Use the Sn formula to find the sum of the first 20 terms.
3. The answer is 1510.
If you need more help, just let me know. Hope you learned how to do similar problems in the future.
1. do 31 times 0.25 = 7.75..then times 7.75 by 4 = 31
Answer – $31.00
2. 3, 6, 9, 12 and 15 def is not sure about 5, 5, 5, 5 and 5.. others are not
3. not a clue:/
5. not a clue:/
6. ???
9. ???
10. ???
go to mathway.com for help great website and gives all answers to any math problem!!!
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