If in a geometric progression an,a1=3,an=96 andSn=189 then the value of n is
5
6
7
8
Explanation for correct option:
Find the value of n:
Given,
a1=3an=96Sn=189
Thenth term of GP is arn-1
3(rn-1)=96⇒rn-1=963⇒rn-1=32⇒rn=32r…(i)
Now,
Sn=a(rn-1)(r-1)⇒a(rn-1)(r-1)=189⇒3(32r-1)(r-1)=189⇒(32r-1)(r-1)=63⇒32r-1=63r-63⇒31r=62⇒r=2
Substituting the value of r in equation i, we get
2n=64⇒2n=26⇒n=6
Hence, the correct option is B.