This week in math, we learned how to find tn in arithmetic sequence when not given t1 and a pattern. first we need to find the difference(how much it goes up by)
for example: your given t2=5 and t5= 11
first you have to find the difference between t2 and t5 (just look at what you have to add from t2 to get to t5).
t2+3d= t5
now substitute the answers of t2 and t5
5+3d=11
now use simple algebra (transfer 5 to the other side)
3d= 11-5
3d=6
divide 3 by both sides
d= 2
now that you know the difference, we can find what tn is using the formula tn=t1+(n-1)d
To find t1 we can just subtract 2 from t2 which equals 3. We know t1 is 3 because the pattern (difference) is 2 and if your going backwards you subtract. substitute all the numbers you know
tn=3+ (n-1)2
tn= 3+2n-2
tn= 2n+1
now you know what tn is.