Question:
The sum of the first 8 terms of a GP is 5 times the sum of its first 4 terms. If r ¹ 1 is the common ratio, then what is the number of possible real values of k?
The sum of the first 8 terms of a GP is 5 times the sum of its first 4 terms. If r ¹ 1 is the common ratio, then what is the number of possible real values of k?
Options:
- a) One
- b) Tw o
- c) Three
- d) More than three
- a) One
- b) Tw o
- c) Three
- d) More than three
correct answer : b)
Explanation:
S8 = 5S4
ar
r
()8 1
1
–
–
= 51
1
4.( )ar
r
–
–
Þ r
r
8
4
1
1
–
–
= 5 Þ rr
r
44
4
11
1
-() +()
–
= 5
Þ r4 = 4 Þ r = ±± 22, i
S8 = 5S4
ar
r
()8 1
1
–
–
= 51
1
4.( )ar
r
–
–
Þ r
r
8
4
1
1
–
–
= 5 Þ rr
r
44
4
11
1
-() +()
–
= 5
Þ r4 = 4 Þ r = ±± 22, i