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### High School Mathematics - 23.15 Sequence and Series - Review

Sequence:
A sequence is a number pattern in a definite order following a certain rule.
It can be denoted by: a1, a2, a3, a4, a5 ..........an-1, an

Series:
Series is a sum of terms in a sequence.
It can be denoted by: a1 + a2 + a3 + a4 + a5 ..........an-1 + an

Series/Sequence are of two types: arithmetic and geometric.

 Arithmetic Geometric The formula to find the nth term is a + (n-1)d a1 rn-1 The formula to find the sum of n terms is S = n/2(a1 + an) S = n/2[a + (n-1)d] S = a1(1 - rn)/(1 - r)
Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ........

Sequences and series can be finite or infinite. A finite sequence/series is one that eventually comes to an end. Infinite sequences/series are those that continue indefinitely.

Examples:
Finite sequence: 1, 5, 9, 13, 17
Finite series: 1 + 5 + 9 + 13
Infinite sequence: 1, 2, 4, 8, 16, . . . . .
Infinite series: 1 + 2 + 4 + 8 + 16 + . . . . .

 Q 1: If a1 = 3, d = 5, and n = 10, what is the value of last term a10 in the arithmetic series?180170200 Q 2: Find the 8th term of 1/8, 1/4, 1/2,..........81016 Q 3: Find the 41st term of the arithhmetic series: 10, 14, 18,..........523848 Q 4: The sum of the first 43 terms of the arithmetic sequence 2, 5, 8,...........128 is_____345127954526 Q 5: Find the 31st term of the arithmetic series 2,5, 8, .....9210287 Q 6: What number term is 384 in the geometric sequence: 3, 6, 12, 24, 48, ........384.6812 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!