Consider the arithmetic sequence log x + log √2, 2 log x + log 2, 3 log x + log 2√2. (a) Find the general term of the sequence.
(b) Find the sum of the first 40 terms of the sequence.

a)

b)

Step-by-step explanation:

Given arithmetic sequence is:

log x + log √2, 2 log x + log 2, 3 log x + log 2√2......

First term a = log x + log √2

common difference d = 2 log x + log 2 - (log x + log √2)

= 2 log x + log 2 - log x - log √2

= log x + log 2 - log √2

= log x + log (√2*√2)- log √2

= log x + log √2 + log √2- log √2

= log x + log √2

(a)

General term of the arithmetic sequence is given as:

(b)

Sum of first n terms of an arithmetic sequence is given as:

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75