Question

an ap consists of n terms the sumof first three terms of ap is 30 and the sum of last three terms is 36 if the first term is 9 then find number of terms​

Answer 1

Answer:

5

Step-by-step explanation:

Sn = n/2[2a+(n-1)d]

S3 = 3/2[2(9)+(3-1)d]

30 = 3/2[18+2d]

30×2=3[18+2d]

60/3=18+2d

20=18+2d

2d=20-18

2d=2

d=2/2

d=1

an=a+(n-1)d

an=9+(n-1)1

an=9+n-1

an=8+n

a(n-1)=a+(n-1-1)d

a(n-1)=9+(n-2)1

a(n-1)=7+n

a(n-2)=a+(n-2-1)d

a(n-2)=9+(n-3)1

a(n-2)=9+n-3

a(n-2)=6+n

S(last 3 term)=an+a(n-1)+a(n-2)

S(last 3 term)=8+n+7+n+6+n

S(last 3 term)=21+3n

36=21+3n

3n=36-21

3n=15

n=15/3

n=5