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SIMPLE WAY TO UNDERSTAND ARITHIMETIC AND GEOMETRIC PROGRESSION...

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PROGRESSIONS:

PROGRESSIONS GEOMETRIC AND ARITHMETIC

ARITHMETIC PROGRESSION:

ARITHMETIC PROGRESSION

FORMULA:

FORMULA A+D(N-1) IN WHICH: A= the beginning number of the sequence. D= the difference between numbers of the sequence (should be the same) N= is the position of the term in the sequence.

FOR EXAMPLE: Q. simple:

FOR EXAMPLE: Q. simple Sequence = 2, 4, 6, 8, 10. Derive a formula to find the n th term. Find the 22 nd term.

SOLUTION:

SOLUTION Therefore: DIFFERENCE=> 2 4 6 8 10 2 2 2 2 now lets use the formula : A+D(N-1)

SOLUTION:

SOLUTION i.e 2+ 2X(n-1) => 2+2n-2 = 2n Therefore 22 nd term = 2X22 = 44

FOR EXAMPLE: difficult:

FOR EXAMPLE: difficult Sequence = 128, 220, 312, 404 Derive a formula to find the n th term. Find the 82 nd term.

SOLUTION:

SOLUTION Therefore: DIFFERENCE=> 128 220 312 404 92 92 92 now lets use the formula : A+D(N-1)

SOLUTION:

i.e 128+ 92X(n-1) => 128+92n-92 = 92n-36 Therefore 82 nd term = 92X82-36 = 7508 SOLUTION

GEOMETRIC PROGRESSION:

GEOMETRIC PROGRESSION

FORMULA:

FORMULA AXR (n-1) IN WHICH: A= the beginning number of the sequence. R= the multiplying factor between numbers of the sequence (should be the same) N= is usually the position of the term in the sequence.

FOR EXAMPLE: Q simple:

FOR EXAMPLE: Q simple Sequence = 2, 6, 14, 30. Derive a formula to find the n th term. Find the next term.

SOLUTION:

SOLUTION Therefore: DIFFERENCE=> 2 6 14 30 4 8 16 4 8 4 now lets use the formula : AXR (n-1) i.e 2X4 (n-1) Therefore next term = 2X4 ( 5-1) = 512