SEQUENCES AND

SERIES(ARITHMETIC)BY MALULEKE PJ

SUM MATHEMATICIAN

•CARL FRIEDRICH GAUSS

• NATURE---DID YOU KNOW: UNDERSTANDING A SEQUENCE, ILLUSTRATED BELOW IS A FIBONACCI SEQUENCE ONE OF THE ANCIENT PATTERNS TO EVER BEING DISCOVERED BY MAN-KIND(JACOBS,2011)

ARITHMETIC SEQUENCE•RIMANDO:IT IS A SEQUENCE IN WHICH THE DIFFERENCE BETWEEN CONSECUTIVE TERMS IS CONSTANT AND HAS THE FORM:

• NOTE: AN ARITHMETIC

SEQUENCE

• EXHIBIT CONSTANT GROWTH

dnadadaa 1,,2,, 1111

ARITHMETIC SEQUENCE•EXAMPLES:

• 1, 4, 7, 10, 13, …

• 6, 11, 16, 21, 26, …

• 14, 25, 36, 47, 58, …

• 4, 2, 0, -2, -4, …

• -1, -7, -13, -19, -25, …

ARITHMETIC SEQUENCE

•GENERAL TERM:

dnaan 11

Example/s:

Find the 50th term of the arithmetic sequence 2, 6, 10, 14, …

ARITHMETIC SERIES•A SERIES IS AN INDICATED SUM OF TERMS OF A SEQUENCE. IF THE TERMS FORM AN ARITHMETIC

SEQUENCE WITH FIRST TERM A1

AND COMMON DIFFERENCE D, THE INDICATED SUM OF TERMS IS CALLED AN ARITHMETIC SERIES. THE SUM OF THE FIRST N TERMS,

REPRESENTED AS SN,

IS(GAUTANI,2011)nnn aaaaaS 1321

ARITHMETIC SERIES•LET SN = A1 + A2 + … +

AN BE AN ARITHMETIC

SERIES WITH CONSTANT DIFFERENCE D, THEN:

2

12 1 dnanSn

ARITHMETIC SERIES•LET SN = A1 + A2 + … +

AN BE AN ARITHMETIC

SERIES THEN 21 n

n

aanS

Example/s:

Find the sum of the first 100 positive even numbers.

Reference: Rimando, K. (2011), Sequences and SeriesJacobs, J. (2011), Patterns and SequencesGautani, V. (2011), Sequences and series and binomial TheoremImages: @windows7, Wikipedia