SOLUTION: Theresa is looking at the board in math class and knows that there is an arithmetie sequence on the board. She can see the first number is 12, but she can't the second, third, or f

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Question 1131195: Theresa is looking at the board in math class and knows that there is an arithmetie sequence on the board. She can see the first number is 12, but she can't the second, third, or fourth numbers. The fifth number is 56. What are the numbers that she cannot see? Explain how you found the numbers.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
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12+4d=56
4d=56-12
4d=44
d=11

If the sequence is arithmetic, then the common difference between terms is 11.
12, 23, 34, 45, 56,

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are 4 gaps between the first term and the fifth term of an AP.


So, each gap is  %2856-12%29%2F4 = 44%2F4 = 11 units long.


Thus the common difference of the AP is 11.


The numbers that she can not see are


    a%5B2%5D = 12 + 11 = 23;

    a%5B3%5D = 23 + 11 = 34;

    a%5B4%5D = 34 + 11 = 45.

Solved.