by Guest » Thu Feb 04, 2016 8:19 am
There are numerous arithmetic progressions where 34 in a term in the sequence.
Any sequence that satisfies the equation a + (n-1)d = 34
If take starting value of 1 and common difference of 1 then 34 is there...
1 + (n-1)*1 = 34
n = 34 .....the 34th term is 34.
If take starting value of 1 and common difference of 2 then 34 is NOT there...
1 + (n-1)*2 = 34
1 + 2n - 2 = 34
2n = 34 + 1
2n = 35
n = 17.5 ... n is not an even number so 34 is NOT there.
If take starting value of 1 and common difference of 3 then 34 is there...
1 + (n-1)*3 = 34
1 + 3n - 3 = 34
3n = 34 + 2
3n = 36
n = 12 ....so 34 is the 12th term in the sequence.
If take starting value of 2 and common difference of 2 then 34 is there...
2 + (n-1)*2 = 34
2 + 2n - 2 = 34
2n = 34
2n = 34
n = 17 ....so 34 is the 17th term in the sequence.
If take starting value of 2 and common difference of 3 then 34 is there...
2 + (n-1)*3 = 34
2 + 3n - 3 = 34
3n = 34 + 1
3n = 35
n = 11.66 .... n is not an even number so 34 is NOT there.
If take starting value of 2 and common difference of 4 then 34 is there...
2 + (n-1)*4 = 34
2 + 4n - 4 = 34
4n = 34 + 2
4n = 36
n = 9 ....so 34 is the 9th term in the sequence.
.....so there are lots and more............