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:

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.