How many numbers are in the list 6, 7, 10, 11, 14, 15,...,94, 95, 98?
There are incrememnts of three every set of two numbers, but I'm not sure how to continue.
listfor(n, 1,24, (4*n+2, 4*n+3))=(6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 34, 35, 38, 39, 42, 43, 46, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 67, 70, 71, 74, 75, 78, 79, 82, 83, 86, 87, 90, 91, 94, 95, 98, 99)
+23245 You can use this formula to help you find the number of terms: tn = t1 + (n - 1)d
tn is the last term of an arithmetic sequence.
t1 is the first term of an arithemtic sequence
n is the number of terms
d is the common difference
This sequence contains two arithmetic sequences:
6, 10, 14, 18, ... 94, 98 and 7, 11, 15, ... 91, 95
In both of these sequences, d = 4.
For 6, 10, 14, 18, ... 94, 98 tn = t1 + (n - 1)d
tn = 98 98 = 6 + (n - 1)4
t1 = 6 92 = 4n - 4
n = unknown 96 = 4n
d = 4 24 = n
For 7, 11, 15, ... 91, 95 tn = t1 + (n - 1)d
tn = 95 95 = 7+ (n - 1)4
t1 = 7 88 = 4n - 4
n = unknown 92 = 4n
d = 4 23 = n
So, there will be a total of 24 + 23 = 47 terms
