## Answers

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**