Numerical Sequence Patterns
SSAT Upper Level · Flashcards · Recall
SSAT UPPER LEVEL · FLASHCARDS
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QUESTION
What is the
n
n
n
th-term formula for an arithmetic sequence with first term
a
1
a_1
a
1
and common difference
d
d
d
?
QUESTION
What is the explicit formula for the
n
n
n
th triangular number
T
n
T_n
T
n
?
QUESTION
What is the
n
n
n
th-term formula for a geometric sequence with first term
a
1
a_1
a
1
and ratio
r
r
r
?
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ANSWER
a
n
=
a
1
r
n
−
1
a_n = a_1 r^{n-1}
a
n
=
a
1
r
n
−
1
. This formula computes the
n
n
n
th term by multiplying the first term
a
1
a_1
a
1
by the common ratio
r
r
r
raised to the power of
n
−
1
n-1
n
−
1
.
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