[SOLVED] Arithmetic and Geometric progressions

**Webby** · February 25th 2009, 01:49 AM

Having a bit of trouble when it comes to these questions, any help is very much appreciated

Q1. Programming languages such as miranda and Q use the notations [a..b] and [a,b..c] to represent finite sequences. For example, [1..5] is the sequence{1,2,3,4,5} and [1,3..11] is the sequence {1,3,5,7,9,11} (ie the 3 is the second term) For each of the notations [a..b] and [a,b..c], give a formula for the number of terms n of the sequence in terms of a,b and c.

Q2. (a) Are the terms of the sequence Un = {log2,log2^2,log2^3} in arithmetic or geometric progression? What about Vn={(log2),(log2)^2,(log2)^3}?
(b) Find the sum of the first 10 terms of both Un and Vn.

**mathaddict** · February 25th 2009, 03:38 AM

Originally Posted by Webby

Q2. (a) Are the terms of the sequence Un = {log2,log2^2,log2^3} in arithmetic or geometric progression? What about Vn={(log2),(log2)^2,(log2)^3}?
(b) Find the sum of the first 10 terms of both Un and Vn.

(a) $U_n= log2,2log2,3log2,...$ , d=log 2 , thus it is an AP .

$V_n=(log2),(log2)^2,(log2)^3,...$ , r=log2 , it is a GP .

They are both different .

(b) Use the formulas of sum of AP and GP respectively .

**Soroban** · February 25th 2009, 05:56 AM

Hello, Webby!

Q2. (a) Are the terms of the sequence $U_n \:=\:\log2,\;\log(2^2),\:\log(2^3),\:\hdots$
in arithmetic or geometric progression?

We have: . $\log 2,\:2\log2,\:3\log2,\:\hdots$

This is an arithmetic sequence with first term, $a = \log 2$ ,
. . and common difference, $d = \log 2$

(b) What about: $V_n\:=\:(\log2),\:(\log2)^2,\:(\log2)^3,\:\hdots$