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+(n−1)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=(16−2(6))
a1=(16−12)=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 T7−T5=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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