Tuesday, 28 January 2014

Arithmetic progression (given third term and difference between 5th and 7th term)





Given that the 3rd term of an arithmetic progression (AP) is
16 and the difference between the 5th and the 7th term is 12,
write down the first 7 terms of the AP.




For an AP, the nth term is given by:



an=a+(n1)d




where a is the first term and d is the common difference



The difference between the 5th and the 7th is 12



12/2=6



a3=a+2d=16



a3=a+2(6)=16




a1=(162(6))



a1=(1612)=4



Is this the correct method to find the first term?


Answer



Assuming that the 7th term is greater than the 5th term, we have the following:



Note that T1,T3,T5,T7 are also in AP (AP2).




Given that T3=16, and T7T5=12 (i.e. common difference for AP2 is 12), we have T1,3,5,7=4,16,28,40.



Interpolating (since an AP is linear) we have



T1,2,3,4,5,6,7=2,4,10,16,22,28,34,40


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