What is the next term in the sequence: #sqrtx/3, (2sqrtx)/3, sqrtx,...#?
#sqrt(x)/3, (2sqrt(x))/3, sqrt(x)#
We could also write this as:
#(1sqrt(x))/3, (2sqrt(x))/3, (3sqrt(x))/3#
This is an arithmetic sequence, with common difference
So (if it continues as an arithmetic sequence) the next term is formed by adding the common difference.
#(3sqrt(x))/3 + sqrt(x)/3 = (4sqrt(x))/3#
Next term, I.e. the
Similarly, difference between
Therefore, the common difference between successive terms
This is an arithmetic progression (A.P) with
Sa_n = a + ((n-1)*d) #