Let an be an arithmetic progression with a4 + a7 + a10 = 17 and a4 + a5 +···+ a13 + a14 = 77. if ak = 13, then k =?

The value of k is 18.

Step-by-step explanation:

Here, the AP is,

Let a be the first term and d is the common difference,

So the arithmetic sequence would be,

Given,

Now,

22 × equation (1) - 3 × equation (2),

We get,

From equation (1),

Here,

By substituting the value,

Hence, the value of k is 18.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

well what did you do it matters what you did : )

step-by-step explanation: