The first term of an arithmetic sequence is 14. the 25th term is 206. find the common difference

We can manipulate the arithmetic sequence formula to solve this problem.

Let's look at  where is the term, is the first term,  is the number of terms, and  is the common difference. We already know that is equal to , is equal to , and is equal to . This therefore leave us with only the common difference to solve.

Manipulating the formula we can arrive at the




ANSWER: The common difference is 8.

6400

Step-by-step explanation:

Given the profit function ;

P(c) = –20c2 + 320c + 5,120

The maximum value is given by :

f(h) ; where, h = - b /2a

From P(C) ; a = - 20 ; b = 320

h = - b / 2a = - 320 / 2(-20) = - 320 / 40 = 8

c = h

P(8) = –20(8)² + 320(8) + 5,120

P(8) = - 1280 + 2560 + 5120

= 6400