Question

The second and fifth terms of a geometric progression(G.P. ) are 1 and 1/8 respectively find the first term and eight term.

Answer 1

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

Answer 2

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Answer 3

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