Since this is an arithmetic sequence, you get the common difference 'd'.
d = 7.5 - 6 = 1.5
or 6 - 4.5 = 1.5
d = 1.5
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A1 as given is 3
Sn = 156
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you have the formula for the sum of arithmetic sequence as
Sn = [2A1 + (n-1) d] n/2
156 = [2 (3) + (n-1) 1.5] n/2
156 (2) = [6 + 1.5n - 1.5] n
312 = [1.5n + 4.5] n
312 = 1.5n^2 + 4.5n
1.5n^2 + 4.5n - 312 = 0
divide the whole equation with 1.5
n^2 + 3n - 208 = 0
(n+16)(n-13) = 0
n = -16
n = 13
take the positive value.
therefore there are 13 terms in the sequence
