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Fill in the blanks. The next two numbers in the pattern: 1, 8, 27, 64, 125, ___, ____. The cube of an odd number is always ______. The cube of a negative integer is _______. The last digit of a number which has 3 as last digit in its cube is ______. |
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Answer» Answer: We can also formulate this This is called a geometric sequence, where the next term can be obtained by multiplying the prior term by a paricular number, called a common ration... So if a is our FIRST term, and is our common ration, then our sequence would look like... a , a r , a r 2 , a r 3 ... .
This has an n t h term of: a ⋅ r n − 1 where the first term is at n = 1
Your sequance is: − 5 , − 10 , − 20 , − 40 ...
So a = − 5 and r = 2
n t h term = ( − 5 ) ⋅ 2 n − 1
So our next terms our n = 5 and then n = 6
So hecne using the formula: -80, -160 are the next two terms We can also take a sum of the first n terms, but thats a DIFFERENT STORY...!
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