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) ,

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

For 1 flavor there are 9 topping

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

No of choices= 5*9

=45 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

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.

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The answer is in the image 

Volume of rectangular prism=length * width * height

Given,

length=3/8cm

breadth=5/8cm

height=7/8cm

therefore volume=(3/8)*(5/8)*(7/8)

                           =105/512 cm3