Sequences, Arithmetic and Geometric Progressions

Question

Solve the ff: using the formula for sequences. 1. Given a sequence of numbers: 1 , 5, 9…….. Find : a. the 15th term b. the sum from first to 15th term. 2. Given 3, 9, 15………. Find : a. the 20th term b. the sum from first to 20th term. 3. Given a geometric progression : 2, 6 , 18…. a. find the 21st term b. the sum up to the 21st term

Answer 1

AP, a1=1, d=4,

a15 = 1+4(14) = 57

s15 = (15)(1+57)/2 = 15(29)= 435

AP. a1=3, d=6

a20 = 3+6(19) = 117

s20 = 19(3+117)/2 = 19(60) =1140

GP, a1=2 r=3, n=21

a21 = 2(3^20)= about 2(3.4867844 x 10^9) = about 6.935688 x 10^9 = 21st term

s21= 21(2+6.935688 x 10^9)/2 = sum of 21 terms