a geometric progression or known as a geometric sequence is define as a sequence of numbers which has a common ratio, it means each term after the first is a product of the previous term and a constant value (r), r is non-zero number called the common ratio.

Geometric Sequence Formula for finding the nth term

an=a1⋅r^(n−1), the formula for finding nth term

Find r

an = a1•r^(n-1)

a3 = 8

a8 = ¼

8 = a1•r^(3-1)

8 = a1•r²

a1 = 8/r²

¼ = a1•r^(8-1)

¼ = a1•r⁷

a1 = ¼/r⁷

¼/r⁷ = 8/r²

1/4r⁷ = 8/r²

r² = 32r⁷

r²/r⁷ = 32

1/r⁵ = 32

r⁵ = 1/32

r = 1/2

Find First Term

a1 = 8/r²

a1 = 8/(½)²

a1 = 8/¼

a1 = 32

Final Answer:

First Term is 32

First Term is 32Common Ratio is 1/2

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