Question

The sum of 1st three terms an AP is 30 and the sum of last three terms is 39.If the 1st term is 9,then find the number of terms in AP

Answer 1

Let the first 3 terms be a, a+d, a+2d.

Now, sum of 3 terms is 30

So:- a + (a+d) + (a+2d) = 30

=> 3a + 3d = 30

=> a + d = 10

given a=9

=>d=10-9=1

If n is the no.of terms

last term will be =a+(n-1)d =9+(n-1)*1=8+n

2nd last term will be =a+(n-2)d=9+(n-2)*1=7+n

3rd last term will be =a+(n-3)d=9+(n-3)*1=6+n

Given sum of last 3 terms=39

=>6+n+7+n+8+n=39

=>21+3n=39

=>3n=39-21=18

=>n=18/3=6

therefore no.of terms,n=6 ,a=9,d=1

So the AP is 9,10,11,12,13,14

The sum of 1st three terms =9+10+11=30

the sum of last three terms =12+13+14=39