Answer:
See below ~
Step-by-step explanation:
<u>Solving for x in ΔLMN</u>
- 6x + 3 + 4x - 10 + 5x + 7 = 180
- 15x = 180
- x = 12
<u>Angles in ΔLMN</u>
- (6x + 3)° = 6(12) + 3 = 75°
- (4x - 10)° = 4(12) - 10 = 38°
- (5x + 7)° = 5(12) + 7 = 67°
<u>Solving for y in ΔSTU</u>
- 5x + 3y + 9y - 7 + 6x - 5 = 180
- 11x + 12y - 12 = 180
- 11(12) + 12y = 192
- 132 + 12y = 192
- 12y = 60
- y = 5
<u>Angles in ΔSTU</u>
- (5x + 3y)° = 5(12) + 3(5) = 60 + 15 = 75°
- (9y - 7)° = 9(5) - 7 = 45 - 7 = 38°
- (6x - 5)° = 6(12) - 7 = 72 - 7 = 67°
⇒ Their angles are equal (in ΔLMN and ΔSTU)
⇒ ΔLMN and ΔSTU are similar
Third term = t3 = ar^2 = 444 eq. (1)
Seventh term = t7 = ar^6 = 7104 eq. (2)
By solving (1) and (2) we get,
ar^2 = 444
=> a = 444 / r^2 eq. (3)
And ar^6 = 7104
(444/r^2)r^6 = 7104
444 r^4 = 7104
r^4 = 7104/444
= 16
r2 = 4
r = 2
Substitute r value in (3)
a = 444 / r^2
= 444 / 2^2
= 444 / 4
= 111
Therefore a = 111 and r = 2
Therefore t6 = ar^5
= 111(2)^5
= 111(32)
= 3552.
<span>Therefore the 6th term in the geometric series is 3552.</span>
Answer:
The first one on the left
Step-by-step explanation: