The 8th term of a gp is _7/32. find its common ratio if its first term is 28.

3 answers

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a1 = 28

a8 = a1 ∙ r ⁷

7 / 32 = 28 ∙ r ⁷

Divide both sides by 28

( 7 / 32 ) / 28 = r ⁷

7 / 32 ∙ 28 = r ⁷

7 / 32 ∙ 7 ∙ 4 = r ⁷

1 / 32 ∙ 4 = r ⁷

1 / 128 = r ⁷

r = ⁷√ ( 1 / 128 )

r = ⁷√ 1 / ⁷√ 128

r = 1 / 2
28