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) ,

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The total nom of  code that can be used is equal to 5+3 = 8

The answer is in the image 

The answer is in the image 

The solution is given in the image below

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.