Arithmetic Sequence a, a + d, a + 2d, a + 3d….. an = a + (n – 1) d a. Find the nth term of the sequence 2, 5, 8….. a =2 d=3 an = a + (n – 1) d an = 2 + (n – 1) 3 b. Find the 25th term in the sequence of 5, 11, 17, 23, 29 . . . n =25 a = 5 d = 6 a2 – a1 = 11 - 5 = 6 an = a + (n – 1) d a25 = a + (n – 1) d a25 = 5 + (25 – 1) 6 a25 = 5 + (24) 6 a25 = 5 + 144 a25 = 149 25th term of the given sequence c. Find the first term of an arithmetic sequence if the 9th term is 72 and the common difference is 5. a9 = 72 n = 9 d =5 a1 =? an = a + (n – 1) d 72 = a1 + (9 -1)5 72 = a1 + (8)5 72 = a1 + 40 72 – 40 = a1 32 = a1 1st term of the given sequence a1 = 32 1st term of the given sequence Geometric Sequence a, ar, ar2, ar3, ar4…. an = arn-1 r= 𝑎𝑛+1 𝑎𝑛 1. Find the nth term, the fifth term, and the 100th term, 1 of the geometric sequence determined by a = 6 and r = 3 . a. For nth term an = arn-1 1 3 an = 6( )n-1 6 an = (3)n-1 an = 2𝑛−1 nth term of the geometric sequence b. For fifth term an = arn-1 1 a5 = 6(3)5-1 1 a5 = 6(3)4 1 a5 = 6(34 ) 1 a5 = 6(81) a5 = a5 = 6 81 2 27 5th term of the geometric sequence c. For 100th term an = arn-1 1 a100 = 6(3)100-1 1 a100 = 6(3)99 1 a100 = 6(399 ) 6 a100 = 399 = a100 = 2𝑥3 399 2 398 = 2𝑥3 399 2 = 398 100th term of the geometric sequence 2. Find the common ratio, the fifth term and the nth term of the geometric sequence -1, 9, -81, 729…. a. For common ratio a = -1 9 r = −1 = -9 common ratio b. For fifth term a5 = a4 ● r a5= 729 (-9) a5 = -6,561 5th term of the geometric sequence c. For nth term an = arn-1 an = (-1)(-9) n-1 nth term of the geometric sequence