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MATH / The sequence (a_(n)) is defined by a₁=14 and

Problem

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problem

The sequence (an)(a_n) is defined by a1=14a_1 = 14 and an=24−5an−1a_n = 24 - 5a_{n - 1}for all n≥2.n \ge 2. Then the formula for the nnth term can be expressed in the form an=p⋅qn+r,a_n = p \cdot q^n + r, where p,p, q,q, and rr are constants. Find p+q+r.p + q + r.
Plain-text mathematical notation (without MathML)
The sequence (a_(n)) is defined by a₁=14 and
a_(n)=24−5a_(n−1)for all n≥2.  Then the formula for the nth term can be expressed in the form a_(n)=p⋅q^(n)+r, where p, q, and r are constants.  Find p+q+r.
Original LaTeX notation
The sequence $(a_n)$ is defined by $a_1 = 14$ and
\[a_n = 24 - 5a_{n - 1}\]for all $n \ge 2.$  Then the formula for the $n$th term can be expressed in the form $a_n = p \cdot q^n + r,$ where $p,$ $q,$ and $r$ are constants.  Find $p + q + r.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
6f585924-0597-5bd0-9fe7-ebb7eccff4fd
task_key
intermediate~5falgebra--test--6f585924-0597-5bd0-9fe7-ebb7eccff4fd
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import