a geometric progression with a positive common ratio is such that the sum of the first two terms is 8 and the third term is 18. find the common ratio?
Answers
Answer:
the sum of the four terms of the geometric series be a+ar+ar
2
+ar
3
and r>0
Given that a+ar=8 and ar
2
+ar
3
=72
Now, ar
2
+ar
3
=r
2
(a+ar)=72
⇒r
2
(8)=72∴r=±3
Since r>0, we have r=3.
Now, a+ar=8⇒a=2
Thus, the geometric series is 2+6+18+54.
Step-by-step explanation:
the sum of the four terms of the geometric series be a+ar+ar
2
+ar
3
and r>0
Given that a+ar=8 and ar
2
+ar
3
=72
Now, ar
2
+ar
3
=r
2
(a+ar)=72
⇒r
2
(8)=72∴r=±3
Since r>0, we have r=3.
Now, a+ar=8⇒a=2
Thus, the geometric series is 2+6+18+54.
Answer:
Three
Step-by-step explanation:
Any term of GP= First term * (Common ratio)^n-1
or
nth term= a* r^n-1
therefore sum of two terms=a+ar=8
and ar^2=18
Solving above two we have r^2/1+r=9/4
4r^2=9+9r solve using quadratic splitting factorisation method
we have factors as 12 and -3
Hence r=3 and -3/4 as positive r=3