sequence

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence. Given a first...

Look at this sequence: 53, 53, 40, 40, 27, 27, ... What number should come next? This looks like a sequence where we subtract 13 and then 0, 13 and then 0 from the prior number. Since the last group of 27 repeated, our next number is found by subtracting 13: 27 - 13 = 14

can you continue this pattern 1,5,13,29 Looking at the numbers, we see a pattern of the next number as the prior number * 2 and then add 3 With each term as t(n), we find t(n + 1) as: t(n + 1) = 2*t(n) + 3 t(2) = 2(1) + 3 = 2 + 3 = 5 t(3) = 2(5) + 3 = 10 + 3 = 13 t(4) = 2(13) + 3 = 26 + 3 =...

ADG,BEH,CFI,___,___,___ Looking at this pattern, we see: the first term starts with A and increments by 1 letter the second term starts with D and increments by 1 letter the third term starts with G and increments by 1 letter So terms 4, 5, and 6 are: DGJ EHK FIL

Find the explicit formula of the sequence 3,12,48 We type in 3,12,48 into our search engine. Choose series, and we get: a(n) = 3 * 4^(n - 1)

31,29,24,22,17 what comes next We see that each sequence term alternates between subtracting 2 and subtracting 5. Since the last term, 17, was found by subtracting 5, our next term is found by subtracting 2 from 17: 17 - 2 = 15

1, 9, 25, 49, .......... What is next 1^2 = 1 3^2 = 9 5^2 = 25 7^2 = 49 So this pattern takes odd numbers and squares them. Our next odd number is 9: 9^2 = 81

Oakdale School is sponsoring a canned food drive. In the first week of the drive, the students collected 638 cans. They collected 698 cans in the second week and 758 cans in the third week. If the students continue to collect cans at this rate, in which week will they collect more than 1,000...

Annie got a new video game. She scored 152 points on the first level, 170 points on the second level, 188 points on the third level, and 206 points on the fourth level. What kind of sequence is this? This is an arithmetic series as seen on our calculator:

The next number in the series 38 36 30 28 22 is Notice the change of factors. Subtract 2, Subtract 6, Subtract 2, Subtract 6. So the next number should subtract 2. 22 - 2 = 20

The teacher is handing out note cards to her students. She gave 20 note cards to the first student, 30 note cards to the second student, 40 note cards to the third student, and 50 note cards to the fourth student. If this pattern continues, how many note cards will the teacher give to the fifth...

The next number in the series 2,5,11,20,32,47, is 2 + 3 = 5 5 + 6 = 11 11 + 9 = 20 20 + 12 = 32 32 + 15 = 47 Notice the addition pattern: 3, 6, 9, 12, 15 This means our next term is: 47 + (15 + 3) 47 + 18 65

Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2) a) Find S10 and S∞ b) If the common difference in an arithmetic sequence is twice the first term, show that Sn/Sm = n^2/m^2 a) Sum of the geometric sequence is a = 3 and r = 1/3 (a(1 - r)^n)/(1 - r) (3(1 - 1/3)^9)/(1 - 1/3) S10 =...