Answer:
20 , 20 , 30 will produce a triangle
Step-by-step explanation:
* Lets study how to know if the lengths of the three segments
can formed a triangle
- It is a fact that in any triangle the sum of the smallest two sides
must be greater than the largest side
- Lets study some examples
# If the lengths of the three segments are 5 , 6 , 7
∵ 5 and 6 are the smallest
∴ 5 + 6 = 11
∵ 11 > 7 ⇒ the sum greater than the 3rd side
∴ 5 , 6 , 7 can formed a triangle
# If the lengths of the three segments are 5 , 7 , 12
∵ 5 and 7 are the smallest
∴ 5 + 7 = 12
∵ 12 = 12 ⇒ the sum equal the 3rd side
∴ 5 , 7 , 12 can not formed a triangle
# If the lengths of the three segments are 10 , 12 , 24
∵ 10 and 12 are the smallest
∴ 10 + 12 = 22
∵ 22 < 24 ⇒ the sum less than the 3rd side
∴ 10 , 12 , 24 can not formed a triangle
* Now lets solve the problem
∵ The length of the three segments are 20 , 20 , 30
∵ 20 and 20 are the smallest
∴ 20 + 20 = 40
∵ 40 > 30 ⇒ the sum greater than the 3rd side
∴ 20 , 20 , 30 will produce a triangle
is the first term of the series,
is the common ratio of the series, and
is the number of terms in this series.