Question

Q. 8. Answer the following:
(a) Write the steps to plot a column chart for the
data given in the table below which shows
the distance of five cities from Chandigarh:
Name of
Distance
the city
in km
Ambala
170
Delhi
280
Jalandhar
150
Jaipur
580
Lucknow 680​

Answer 1

Answer:

x,y,z are in GP so,

and r in common factor.

y=x*r^1

z=x*r^2.

x^p=y^q=z^s ------------(1)

putting above values of y & z in equation (1)

x^p=x^q *r^q=z=x^s*r^2s.

=> x^p=x^q *r^q.

x^(p-q)=r^q. ---------------------(a)

also, x^q *r^q=z=x^s*r^2s.

so,

x^(q-s)=r^(2s-q). -------------------------(b)

and,

x^p=x^s*r^2s.

=> x^(p-s)=r^2s.--------------------------(c)

taking log on both side in equation a,b,c.

we get,

(q-s)logx=(2s-q)logr. -------------(i)

(p-q)logx=qlogr.--------------------(ii)

(p-s)logx=2slogr.-------------------(iii)

dividing iii & ii

we get

(p-q)/q=(p-s)/2s.

2sp-2sq=pq+qs.

=>2sp=qp+qs.

dividing both side by pqs.

we get

2/q=1/s+1/p.

hence it is in AP.