series & sequence

1.if a,b,c be the pth, qth and rth terms respectively of an A.P ,prove that a(q-r)+b(r-p)+c(p-q)=0

2.how many terms are identical in the two Arithematic progression 2,4,6,8..... up to 100 terms and 3,6,9 ..... up to 80 terms.

3 Answers

The 1st sum is a std board level problem that we used to do from our school text books.

2) How many solutions are there (natural) to the eqn 2x=3y, with 1â‰¤xâ‰¤100 and 1â‰¤yâ‰¤80 ?

2. i can simply be said number of multiples of 6 till 200.

a=x+pd
b=x+qd
c=x+rd

Here I have taken x=first term - common difference

d is the common difference

Keep in mind that this trick used is very useful to make the question simpler...

Now simply use the differences above to get the answer...

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