"The sum of the first three terms of a finite geometrical series is -7/10 and their product is -1/125. [Hint: use a/r, a and ar to represent the first three terms, respectively.] The three numbers are ____,_____ and ____.
Answers
Answer:
sorry mate I don't know the answer sorry...becaz I am not good at it
Answer:
-1/10, -1/5, -2/5
Step-by-step explanation:
As per the hint, the three terms take the form a/r, a and ar, for some choice of a and r. Then...
Their product is -1/125
⇒ a/r × a × ar = -1/125
⇒ a³ = -1/125 = (-1/5)³
⇒ a = -1/5
and...
Their sum is -7/10
⇒ a/r + a + ar = -7/10
⇒ a (1/r + 1 + r) = -7/10
⇒ 1/r + 1 + r = -7/10 × 1/a = -7/10 × -5 = 7/2
⇒ 1/r + r = 7/2 - 1 = 5/2
⇒ 1 + r² = (5/2)r
⇒ 2r² - 5r + 2 = 0
⇒ r = ( 5 ± √(5² - 4×2×2) ) / (2×2) = ( 5 ± 3 ) / 4 = 8/4 or 2/4
⇒ r = 2 or 1/2.
Take r=2 (taking r=1/2 just reverses the order of the first three numbers, but what the numbers are is still the same).
The three numbers are then
a/r = -1/10
a = -1/5
ar = -2/5