Question
In a geometric progression, the first term is a and the common ratio is r. The sum of the first two terms is 12 and the third term is 16.
determine the ratio ar^2/a+ar
determine the ratio ar^2/a+ar
Answers
Bosnian
In G.P:
an = a ∙ r ⁿ ⁻ ¹
a1 = a
a2 = a r¹ = a r
a3 = a r²
The sum of the first two terms is 12 means:
a1 + a2 = 12
a + a r = 12
The third term is 16 means:
a3 = a ∙ r² = 16
a r² / ( a + a r ) = 16 / 12 = 4 ∙ 4 / 4 ∙ 3 = 4 / 3
an = a ∙ r ⁿ ⁻ ¹
a1 = a
a2 = a r¹ = a r
a3 = a r²
The sum of the first two terms is 12 means:
a1 + a2 = 12
a + a r = 12
The third term is 16 means:
a3 = a ∙ r² = 16
a r² / ( a + a r ) = 16 / 12 = 4 ∙ 4 / 4 ∙ 3 = 4 / 3