Predict the Nth Term in the Sequence A mathematical model can be made when dealing with a sequence or a series of logarithms. The model should be able to predict the nth term in the sequence and shou
Predict the Nth Term in the Sequence A mathematical model can be made when dealing with a sequence or a series of logarithms. The model should be able to predict the nth term in the sequence and shou
( (2, (78125 (C (Logabx) (in (p/q (part (the (which ) * + , -1 -3 - . 0 0. 0.8982444017... 0.8982444017… 1 16, 16,807 2 2, 2Log3264 3 3, 3.401… 3.786… 32, 35 35: 3x 4, 5. 51 57). 64, 7 73. 75, 75. 7th 8, 9 = =0.8982444017… A Again, Another As C Conclusion D D, D: Denominator: Each Expression First For From Given Here I If Investigation Lets Let’s Like Log(1/125)125 Log(1/5)125 Log(1/625)125 Log(a) Log(b) Log(b). Log(x) Log-1288 Log-1562525 Log16512 Log16807343 Log16807343. Log2 Log25 Log2512 Log28 Log3(-1) Log30 Log3264 Log34349 Log35 Log36216 Log464 Log48 Log4949 Log6216 Log7343, Log749 Log7812525 Log8512 Log864 Log88 Logabx Logabx. Logm2mk Logm3mk Logm4mk Logm5mk Logm6mk Logmmk Log¬12525 Log¬168 Log¬24381 Log¬2525 Log¬2781 Log¬28 Log¬312525 Log¬328 Log¬381 Log¬48 Log¬525 Log¬62525 Log¬648 Log¬72981 Log¬8181 Log¬88 Log¬981 Log¬abx Log¬¬525, Mathematical More No Now Now, Nth Numerator: Same Sequence Since Studying Term Term: Testing That The There Therefore, This To We When While With a a, able acceptable. adding also an analyzing and answer answer. answers answers, answers. any are are, argument around arrive arrived as assume at away b b, back base base) basic be be. before. bottom: break by c calculate can cancelling cannot cases), certain change changed clean, come complex component components computation conclusion! constant constant, convert correctly create creates d. dealing denominator denominator. deriving does down earlier. either end equal equation equations. example example, example. exponential exponentially exponentially. expresses find finding first five follow following for form). form. forms formula formulas found four fraction fraction, from future general get given go go, goes greater happening, have however, in increased increases interesting interesting, into is it its keeping leaves left-hand less lets let’s like limitations log logab, logabx logarithm logarithms logarithms, logarithms. logax logax’ logb1a1 logbnak logbx logbx) logbx’ logs: lower lowest, made main make manipulate many mathematical model models modified more most much multiply must n. ne need negative never no non-decimal not nth number number, numbers. numerator oPredict of on on) one one, one. only operation or original other our out outcome over p pattern pattern, pattern. patterns patterns. perform placed point possible power predict produce produced product proved q raise reduce: reduced reducing remains replacement, replacing rest result return rid right-hand rule, same say second second. section see, sequence sequence, sequences sequences: sequences”. series series. should side side. simpler simplified simplify: simply six solution some starting starts statement steps sum take takes term term, term: terms terms. than that that: the then there third this three time to topic; true). turn two types up use usually value value. variable variables. version very was way we what when where which while why will with with: work. working x you zero zero, zero. ‘C ‘C’ ‘D ‘D’. ‘X’ ‘a’ ‘b’ ‘x’ “More …), Log(a) Log(b) Log216216
Predict the Nth Term in the Sequence
A mathematical model can be made when dealing with a sequence or a series of logarithms. The model should be able to predict the nth term in the sequence and should correctly return its value. Given logab, we can manipulate the variable ‘a’ while keeping b constant, which will produce a pattern.
Mathematical Investigation
Here are some of the basic patterns.
Log¬28 = Log¬48 = Log¬88 = Log¬168 = Log¬328 = Log¬648 = Log-1288 =
Log¬381 = Log¬981 = Log¬2781 = Log¬8181 = - Log¬24381 = Log¬72981 =
Log¬525 = Log¬2525 = Log¬12525 = Log¬62525 = Log¬312525 = Log-1562525 =
Logmmk Logm2mk Logm3mk Logm4mk Logm5mk Logm6mk
As you can see, the ‘b’ value remains constant while the ‘a’ value increases exponentially. With this happening, the outcome is produced from a pattern. The first answer for Log¬28 is . Each time the value of ‘a’ is changed exponentially (2, 4, 8, 16, 32, 64, …), the denominator is