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Number Sequences Problems - easy
Problem №1
The sequence
is defined as
and
for
. Find
Solution:
means that
, therefore
Problem №2
Find
if
,
and
.
Solution:
The recurrence relation is
and its characteristic equation is
with a double root
. It means that
. But any sequence whose explicit member formula is a linear function is an arithmetic progression. Therefore
is the arithmetic progression, defined by
and
. Then
Problem №3
If
, find
Solution:
Problem №4
. Calculate
.
Solution:
Problem №5
. Find
Solution:
Problem №6
Let the sequence
be defined as
. Is it increasing or decreasing?
Solution:
, so the sequence is increasing.
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