Which of the arithmetic sequences contain the terms 91? Show work for all and how you solved the sequences.
a. tn= 6+17n
b. 420,417,414,...
c. t1= 4, d= 7
d. 2, 11, 20,...
6 years ago
Answered By Kazi A
Let's say a certain number x, does belong in sequence:
$t_n=t_1+dn$tn=t1+dn
Let's say this happens at the $m^{th}$mth term, so that $x=t_m$x=tm
This means that $x=t_1+dm$x=t1+dm
or: $\frac{x-t_1}{d}=m$x−t1d=m
In other words, if x is in the sequence, the fraction on the left hand side of the equation above MUST be equal to some positive integer. If it isn't an integer, it cannot be in the sequence.
For example, for the 4th sequence, t1 = 2, d = 9. To check if 91 is in the sequence, we do:
(91 - 2)/9 =89/9 = 9.888...
which is not a positive integer and therefore does not contain the number 91. Check all sequences until you get an integer.
6 years ago
Answered By Kazi A
Let's say a certain number x, does belong in sequence:
$t_n=t_1+dn$tn=t1+dn
Let's say this happens at the $m^{th}$mth term, so that $x=t_m$x=tm
This means that $x=t_1+dm$x=t1+dm
or: $\frac{x-t_1}{d}=m$x−t1d =m
In other words, if x is in the sequence, the fraction on the left hand side of the equation above MUST be equal to some positive integer. If it isn't an integer, it cannot be in the sequence.
For example, for the 4th sequence, t1 = 2, d = 9. To check if 91 is in the sequence, we do:
(91 - 2)/9 =89/9 = 9.888...
which is not a positive integer and therefore does not contain the number 91. Check all sequences until you get an integer.