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the common difference is 2.
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Prove that no matter what the real numbers a and b are the sequence with n th term a + nb is always an AP.find the common difference?
solution:
n th term, tn = a+ nb
n=0, t0 = a + 0×b = a
n=1, t1 = a + 1b = a+b
common difference = t1-t0 = a+b -a = b...........(1)
if n= n-1
then, t(n-1) = a + (n-1)b = a + nb - b
common difference = tn - t(n-1) = a + nb - (a + nb - b) = a + nb - a - nb + b = b.........(2)
from both (1) and (2) common difference, no matter what the real numbers a and b, is b
solution:
n th term, tn = a+ nb
n=0, t0 = a + 0×b = a
n=1, t1 = a + 1b = a+b
common difference = t1-t0 = a+b -a = b...........(1)
if n= n-1
then, t(n-1) = a + (n-1)b = a + nb - b
common difference = tn - t(n-1) = a + nb - (a + nb - b) = a + nb - a - nb + b = b.........(2)
from both (1) and (2) common difference, no matter what the real numbers a and b, is b
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