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MATH / A sequence of positive real numbers {a₁,a₂,a₃,…} has the property that for i≥2, each a_(i) is equal to the sum of all the previous terms. If a₁₉=99, then what is a₂₀?

Problem

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problem

A sequence of positive real numbers {a1,a2,a3,…}\{a_1, a_2, a_3, \dots\} has the property that for i≥2,i \ge 2, each aia_i is equal to the sum of all the previous terms. If a19=99,a_{19} = 99, then what is a20a_{20}?
Plain-text mathematical notation (without MathML)
A sequence of positive real numbers {a₁,a₂,a₃,…} has the property that for i≥2, each a_(i) is equal to the sum of all the previous terms.  If a₁₉=99, then what is a₂₀?
Original LaTeX notation
A sequence of positive real numbers $\{a_1, a_2, a_3, \dots\}$ has the property that for $i \ge 2,$ each $a_i$ is equal to the sum of all the previous terms.  If $a_{19} = 99,$ then what is $a_{20}$?

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
a894c154-479a-5e32-9739-f30a36d81296
task_key
intermediate~5falgebra--test--a894c154-479a-5e32-9739-f30a36d81296
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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