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