Question

SOMEONE PLS HELP ME !!! :(((
1) Write the rule for the nth term of the arithmetic sequence.
3, (-1) , (-5) , . . .
2) write a rule for the nth term of the arithmetic sequence with a_1=-7 and the common difference of 5/2 .
a few moments ago

Answer 1

1) Because the sequence is arithmetic, you know that the nth term is ax+b. The first term is 3=a+b. The second is -1=2a+b. Subtracting the first equation from the second you get -4=a. Insert this value into the first equation to get 3=-4+b; b=7. In conclusion, the nth term is ax+b=-4x+7.

Answer 2

True !

Answer 3

It's good to learn this technique because it applies to other kinds of sequences as well, like quadratic (ax^2+bx+c), cubic and so on.

Answer 4

Yea sometimes I get mixed up. It's good to make a mistake though because then you learn from others like yourself! @JoelSjogren lol ;)

Answer 5

1) Edit: replace x by n.

2) A common way to write the nth term is a_n. It's basically the same story here: a_n = an+b. a_1 is both -7 and a+b. The common difference is both a_(n+1) - a_n = (a(n+1)+b) - (an + b) = (an + a + b) - (an + b) = a and 5/2. We have -7=a+b and a=5/2. Insert the value of a into the first equation to get -7=5/2+b; b = -7-5/2 = -14/2-5/2 = -19/2. In conclusion, a_n = an+b = 5n/2-19/2.