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Paraguay Contests
Paraguay Mathematical Olympiad
2023 Paraguay Mathematical Olympiad
1
1
Part of
2023 Paraguay Mathematical Olympiad
Problems
(1)
a_1, a_2, 78, a_4, a_5, 3438, a_7, a_8,… OMAPA Paraguay 2023.1
Source:
3/26/2024
In the following sequence of numbers, each term, starting with the third, is obtained by adding three times the previous term plus twice the previous term to the previous one:
a
1
,
a
2
,
78
,
a
4
,
a
5
,
3438
,
a
7
,
a
8
,
…
a_1, a_2, 78, a_4, a_5, 3438, a_7, a_8,…
a
1
,
a
2
,
78
,
a
4
,
a
5
,
3438
,
a
7
,
a
8
,
…
As seen in the sequence, the third term is
78
78
78
and the sixth term is
3438
3438
3438
. What is the value of the term
a
7
a_7
a
7
?
algebra