Given that lm is a midsegment of ijk, find jk. a. 7 b. 8 c. 14 d. 16

16

Step-by-step explanation:

We know that segment LM is the mid-segment of the triangle IJK which means ILM is half the size of IJK.

So, IL = LJ.

We know that IL = 7x and LJ = 3x+4 so putting these values equal to each to find the value of x:

7x = 3x + 4

7x - 3x = 4

x =4/4

x = 1

Now, if x = 1, then the segment LM will be:

2x + 6 = 2(1) + 6 = 8

If LM is half the length of JK, then JK is two times the length og LM.

Therefore, JK = 2 * 8 = 16.

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, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for