The 12th term of the arithmetic sequence is 10.5. The 18th term of this sequence is 13.5. Find the common difference and the first term.

let the n'th term be called x, and the value of the term y,

then there is a function y=a*x + b

that will give us all term we want.

this formula is also used for straight lines.

we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula

10.5 = a*12 + b

13.5 = a*18 + b

now lets manipulate these lines.

multiply the first line by 3 and the second line by 2

31.5 = a*36 + 3b

27 = a*36 + 2b

subtract the second line from the first line

4.5 = b

yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.

10.5 = a*12 + 4.5

6 = a*12

0.5 = a

now y=a*x + b can be filled with a and b

y = 0.5 * x + 4.5

for x=1 (the first term) it's f(1)=5

each step is 0.5, hence the common difference.

(13.5-10.5)/(18-12)

= 3 / 6

= 0.5

we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.

from step 12 to step one it's 11 steps down

10.5 - 0.5*11

= 10.5 - 5.5

= 5

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}

p

step-by-step explanation: