Question - If the ratio of the sums of first n^th terms of two AP's is (7n + 1):(4n + 27) find the ratio of their m^th terms.

Answer : The required ratio is (14m-6):(8m+23) .

Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .

That is.

As , we know that the sum of n terms of an AP is given by ,

Assume that ,

Using this we have ,

Now also we know that the nth term of an AP is given by ,

Therefore,

From equation (i) and (iii) ,

Substitute this value in equation (i) ,

Simplify,

From equation (ii) ,

The answer is in the image 

The solution is in the following image

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

The answer is in the image 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image