Answer:
r = 2
Step-by-step explanation:
We have the formula of
Now, it is given that ........ (1)
And we have to find the value of r which satisfy the above equation.
So,
Now, we have to use the trial method to find the value of r.
For r = 1,
Hence, r can not be 1.
Now, put r = 2,
Therefore, r = 2 (Answer)
Answer:
a = , r =
Step-by-step explanation:
The sum to infinity of a geometric progression is
; | r | < 1
Thus for first progression
= 6 ( multiply both sides by (1 - r) )
a = 6(1 - r) → (1)
Second progression
= 7 ← multiply both sides by (1 - r² )
2a = 7(1 - r² ) = 7(1 - r)(1 + r) ← difference of squares
2a = 7(1 - r)(1 + r) → (2)
Substitute a = 6(1 - r) into (2)
2(6(1 - r) = 7(1 - r)(1 + r)
12(1 - r) = 7(1 - r)(1 + r) ← divide both sides by (1 - r)
12 = 7(1 + r) = 7 + 7r ( subtract 7 from both sides )
5 = 7r ( divide both sides by 7 )
r =
Substitute this value into (1)
a = 6(1 - ) = 6 ×
=
