to find whether it is an arithmetic or geometric sequence, let's solve
for arithmetic sequence, let's find the common difference 'd'
1 1/2 - 1 1/4 = 1/4
1 1/4 - 1 = 1/4
d = 1/4
it's an arithmetic sequence but let's recheck if it is also in geometric sequence
..............
find the common ratio 'r'
1 1/2 ÷ 1 1/4 = 1 1/5
1 1/4 ÷ 1 = 1 1/4
since it doesn't have a common ratio then we can conclude that it is indeed an arithmetic sequence
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Given:
An = 9 3/4
A1 = 1
d = 1/4
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to find 'n' we use the formula
An = A1 + (n-1)d
9 3/4 = 1 + (n-1)(1/4)
9 3/4 = 1 + 1/4n - 1/4
9 3/4 = 1/4n + 3/4
9 3/4 - 3/4 = 1/4n
9 = 1/4n
cross multiply 4 to the left
9(4) = n
n = 36
therefore there will be 36 terms
