The simplest answer, the one your teacher is expecting you to give, is based on there being a constant difference of 8 between terms: 145 + 8 = 153, 153 + 8 = 161, so the next number would be 161 + 8 = 169 (in this case t(n) = 137 + 8n).
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However, what number would you like? Give me the next number you want and I'll give you the formula for the terms so that terms 1-3 are as given and the 4th term is the number you want. eg with t(n) = (4n³ - 24n² + 68n + 387)/3, t(1) = 145, t(2) = 153, t(3) = 161, t(4) = 177.
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161
140 becomes 161 when increased by 15%. To find this answer, simply divide 161 by 1.15.
The answer is 485. The pattern is 3x+2 where x is the previous number. For example 3(1) + 2 = 5, 3(5) + 2 = 17, etc. So to figure out the next number you just multiply 3 by 161 and add 2 to get 485.
161 can be divided into several numbers. If you're looking for a whole number, one answer could be 23. Therefor, the quotient would be 7.
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