a1 = the first term
r = common ratio
The n-th term of a geometric sequence:
xn = a ∙ r ⁿ ⁻ ¹
x2 = a1 ∙ r = 1
x5 = a1 ∙ r⁴ = 1 / 8
x5 / x2 =
a r⁴ / a r = ( 1 / 8 ) / 1
r³ = 1 / 8
r = ∛( 1 / 8 ) = ∛1 / ∛8 = 1 / 2
a1 ∙ r = 1
a1 = 1 / r = 1 / ( 1 / 2 ) = 2
a8 = a1 ∙ r⁷ = 2 ∙ ( 1 / 2 )⁷ = 2 ∙ 1⁷ / 2⁷ = 2 ∙ 1 / 128 = 1 / 64
The second and fifth terms of a geometric progression(G.P. ) are 1 and 1/8 respectively find the first term and eight term.
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