SOLUTION: In a sequence of positive integers, each term is larger than the previous term. Also, after the first two terms, each term is the sum of the previous two terms. The eighth term o

Algebra.Com
Question 730737: In a sequence of positive integers, each term is larger than the previous term. Also, after the
first two terms, each term is the sum of the previous two terms.
The eighth term of the sequence is 390. What is the ninth term?
Answer by fcabanski(1391)   (Show Source): You can put this solution on YOUR website!
Call the first term x and the second term y.


1: x


2: y


3: x+y


4: x+y + y = x+2y (added the previous two terms).


5: 2x+3y


6: 3x+5y


7: 5x+8y


8: 8x + 13y = 390
9: 13x+21y


The problem states that the second term, y, is greater than the first term, x. They are both positive and both integers.


Try a few: y = x+1 gives term 8 as:


8x + 13(x+1) = 390


8x + 13x + 13 = 390


21x = 377


x = 377/21 which is not an integer. So y cannot be x+1.


Try y = x+2:


8x + 13(x+2) = 390


8x +13x +26 = 390


21x = 364


364/21 = not an integer.


Now there's a pattern. In each case (y+n), x= (390-13n)/21. It must be an integer.


n = 3, 4, 5, 6, 7, 8 don't work. But n=9 works.


8x + 13(x+9)= 390


8x+13x + 117 = 390


21x = 273


x = 273/21 = (390-13*9)/21 = 13.


x = 13 and y = 13+9 = 22


The 9th term is 13x + 21y = 13(13)+21(22) = 169 + 462 = 631

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

RELATED QUESTIONS

In a sequence each even term is a times than the previous term and each odd term is c... (answered by ikleyn)
In a sequence of numbers each term after the first three terms is the sum of the previous (answered by fcabanski)
3,3,6,9,15,24,..... The first two terms in the sequence above are 3. Each term after... (answered by Boreal)
In a sequence, each term after the first is four more than three times the pervious... (answered by Cromlix)
3, 5,–5... The first term in the sequence of numbers shown above is 3. Each... (answered by Edwin McCravy)
The first two terms of a sequence are a, b. From then on, each term is equal to the... (answered by CharlesG2)
Write the first four terms of a sequence in which the first term is 2 and each term is 6... (answered by checkley77)
The first term in a sequence of number is 2. Each even-numbered term is 3 more than the... (answered by sudhanshu_kmr)
In the seven-term sequence A,B,C,D,E,F,G each term after the first three is the sum of... (answered by solver91311)