The sum of the first twelve terms of arithmetic progression [ap] is 168. if the third term is 7. find the value of the common difference and the first term

Common difference = 2

First term = 3.

Step-by-step explanation:

3rd term = a1 + (3 - 1)d  = 7    where a1 = first term and d = the common difference.

Sum of the first 12 terms = (12/2)[2a1 + (12-1)d] = 168

so 6(2a1 + 11d) = 168

So simplifying, we have the following system:

 a1 + 2d = 7  (A)

12a1 + 66d = 168

2a1 + 11d = 28(B)   Multiplying equation A by - 2:

-2a1 - 4d =- -14                      Adding this to equation B

7d = 14

d = 2

Now plug this into equation A:

a1 + 2(2) = 7

a1 = 7-4

a1 = 3.

answer: 2 and 1

step-by-step explanation: got this question

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (