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MATH / Let a₁, a₂, a₃, … be an arithmetic sequence, and let b₁, b₂, b₃, … be a geometric sequence. The sequence c₁, c₂, c₃, … has c_(n)=a_(n)+b_(n) for each positive integer n. If c₁=1, …

Problem

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problem

Let a1,a_1, a2,a_2, a3,a_3, …\dots be an arithmetic sequence, and let b1,b_1, b2,b_2, b3,b_3, …\dots be a geometric sequence. The sequence c1,c_1, c2,c_2, c3,c_3, …\dots has cn=an+bnc_n = a_n + b_n for each positive integer n.n. If c1=1,c_1 = 1, c2=4,c_2 = 4, c3=15,c_3 = 15, and c4=2,c_4 = 2, compute c5.c_5.
Plain-text mathematical notation (without MathML)
Let a₁, a₂, a₃, … be an arithmetic sequence, and let b₁, b₂, b₃, … be a geometric sequence.  The sequence c₁, c₂, c₃, … has c_(n)=a_(n)+b_(n) for each positive integer n.  If c₁=1, c₂=4, c₃=15, and c₄=2, compute c₅.
Original LaTeX notation
Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence, and let $b_1,$ $b_2,$ $b_3,$ $\dots$ be a geometric sequence.  The sequence $c_1,$ $c_2,$ $c_3,$ $\dots$ has $c_n = a_n + b_n$ for each positive integer $n.$  If $c_1 = 1,$ $c_2 = 4,$ $c_3 = 15,$ and $c_4 = 2,$ compute $c_5.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
5539d29a-a211-54d9-b891-18983e52a636
task_key
intermediate~5falgebra--test--5539d29a-a211-54d9-b891-18983e52a636
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import