SOLUTION: term 1 2 3 4 ... n value 1 3 6 10 .. What is the formula for this puzzle?????

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Question 58694This question is from textbook Algebra 1
: term 1 2 3 4 ... n
value 1 3 6 10 ..
What is the formula for this puzzle????? This question is from textbook Algebra 1

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
term 1 2 3 4 ... n
value 1 3 6 10 ..
What is the formula for this puzzle?????
t1=1
t2=3
t3=6
t4=10
------------------------------
t2-t1=2
t3-t2=3
t4-t3=4
hence
t5-t4=5
t6-t5=6
.......etc
t(n-1)-t(n-2)=n-1
tn-t(n-1)=n
-----------------
adding all
tn-t1=2+3+4+......+n
tn=t1+2+3+4.....n=1+2+3+4......+n=n(n+1)/2
hence
tn = n(n+1)/2
test
t1=1*2/2=1
t2=2*3/2=3
t3=3*4/2=6
t4=4*5/2=10
ok..