Arithmetic and Geometric Sequence PDF

Sequence refers to an ordered list of numbers called terms, that may have repeated values. 1, (1st (2nd 2, 3, (4th (5th 4, term) term) 5…3 term)...

Sequence refers to an ordered list of numbers called terms, that may have repeated values. 1, (1st (2nd 2, 3, (4th (5th 4, term) term) 5…3 term) rd term) term)  Arithmetic Sequence It is a sequence of numbers that follows a definite pattern. To determine if the series of numbers follow an arithmetic sequence, check the difference between two consecutive terms. If common difference is observed, then definitely arithmetic sequence governed the pattern. common difference: 2 2, 4, 6, 8, 10 … 2 2 2 2 15, 20, 25, 30, 35 … cd: 5 5 5 5 14, 36, 58, 80, 102 … cd: 22 22 22 22 30, 56, 82, 108, 134 … cd: 34, 235, 436, 637, 838 … cd: Finding n term of a Arithmet th Sequence Find the 32nd term in the sequence 2, 4, 6, 8, 10 … 𝒂𝒏 =𝒂 𝟏 + ( 𝒏 − 𝟏 ) 𝒅  Find the 32 term in the nd sequence 2, 4, 6, 8, 10 … n = 32 d=2 𝒂𝟑𝟐 =𝟐+ ( 𝟑𝟐 − 𝟏 ) 𝟐 𝒂𝟑𝟐 =𝟐 + ( 𝟑𝟏 ) 𝟐 𝒂𝟑𝟐 =𝟐 + 𝟔𝟐 𝒂𝟑𝟐 =𝟔𝟒  Find the 32 term in the nd sequence 𝒂𝒏 =𝒂 𝟏 + ( 𝒏 − 𝟏 ) 𝒅 𝒂𝟑𝟐 =𝟐+ ( 𝟑𝟐 − 𝟏 ) 𝟐 𝒂𝟑𝟐 =𝟐 + ( 𝟑𝟏 ) 𝟐 𝒂𝟑𝟐 =𝟐 + 𝟔𝟐 𝒂𝟑𝟐 =𝟔𝟒  Find the 65 term in the th sequence 15, 20, 25, 30, 35 … n = 65 d=5 𝒂𝟔𝟓 =𝟏𝟓+ ( 𝟔𝟓 − 𝟏 ) 𝟓 𝒂𝟔𝟓 =𝟏𝟓+ ( 𝟔𝟒 ) 𝟓 𝒂𝟔𝟓 =𝟏𝟓+ 𝟑𝟐𝟎 𝒂𝟔𝟓 =𝟑𝟑𝟓 Find the 65 term in the th sequence 𝒂𝒏 =𝒂 𝟏 + ( 𝒏 − 𝟏 ) 𝒅 𝒂𝟔𝟓 =𝟏𝟓+ ( 𝟔𝟓 − 𝟏 ) 𝟓 𝒂𝟔𝟓 =𝟏𝟓+ ( 𝟔𝟒 ) 𝟓 𝒂𝟔𝟓 =𝟏𝟓+ 𝟑𝟐𝟎 𝒂𝟔𝟓 =𝟑𝟑𝟓 1.Find the 43 term in the rd sequence 14, 36, 58, 80, 102 … n= d= 𝒂𝒏 =𝒂 𝟏 + ( 𝒏 − 𝟏 ) 𝒅 2. Find the 77th term in the sequence 30, 56, 82, 108, 134 … n= d= 𝒂𝒏 =𝒂 𝟏 + ( 𝒏 − 𝟏 ) 𝒅 Geometric Sequence we need to look for the common ratio. All possibilities must be explored until some patterns of uniformity can intelligently be struck. common ratio: 2 2, 4, 8, 16, 32 … x2 x2 x2 x2 Geometric Sequence we need to look for the common ratio. All possibilities must be explored until some patterns of uniformity can intelligently be struck. common ratio: 20 4, 20, 100, 500, 2000 … x20 x20x20x20  8, 40, 200, 1000, 5000, … r: 10, 80, 640, 5120, 40960, … r: Finding n term of a Geometr th Sequence Find the 9th term in the sequence 2, 4, 8, 16, 32 … 𝒏−𝟏 𝒂𝒏 =𝒂 𝟏 𝒓  Find the 9 term in the sequence th 2, 4, 8, 16, 32 … n=9 r=2 𝒏−𝟏 𝒂𝒏 =𝒂 𝟏 𝒓 𝟗− 𝟏 𝒂𝟗 =(𝟐 )𝟐 𝟖 𝒂𝟗 =( 𝟐 ) 𝟐  𝒏−𝟏 𝒂𝒏 =𝒂 𝟏 𝒓 𝟗− 𝟏 𝒂𝟗 =(𝟐 )𝟐 𝟖 𝒂𝟗 =( 𝟐 ) 𝟐 𝒂𝟗 = ( 𝟐 ) 𝟐𝟓𝟔 𝒂𝟗 =𝟓𝟏𝟐 Finding n term of a Geometr th Sequence Find the 11th term in the sequence 4, 20, 100, 500, 2000 … 𝒏−𝟏 𝒂𝒏 =𝒂 𝟏 𝒓  Find the 11 term in the th sequence 4, 20, 100, 500, 2000 … n = 11 r=5 𝒏−𝟏 𝒂𝒏 =𝒂 𝟏 𝒓 𝟏𝟏 − 𝟏 𝒂𝟏𝟏 =(𝟒 )𝟓 𝟏𝟎 𝒂𝟏𝟏 =(𝟒 )𝟓  𝒏−𝟏 𝒂𝒏 =𝒂 𝟏 𝒓 𝟏𝟏 − 𝟏 𝒂𝟏𝟏 =(𝟒 )𝟓 𝟏𝟎 𝒂𝟏𝟏 =(𝟒 )𝟓 𝒂𝟏𝟏 =( 𝟒 ) 𝟗 , 𝟕𝟔𝟓 , 𝟔𝟐𝟓 𝒂𝟏𝟏 =𝟑𝟗 , 𝟎𝟔𝟐 , 𝟓𝟎𝟎  Find the 12 term in the th sequence 3, 9, 27, 81, 243 … n= r= 𝒏−𝟏 𝒂𝒏 =𝒂 𝟏 𝒓 Find the 10 term in the th sequence 2, 14, 98, 81, 243 … n= r= 𝒏 − 𝟏 𝒂𝒏 =𝒂 𝟏 𝒓