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To insert five numbers between 8 and 26 such that the resulting sequence forms an Arithmetic Progression (A.P.), we need to find the common difference first. The common difference (d) of an A.P. is calculated by subtracting the first term from the second term or vice versa.
Let's denote the first term of our A.P. as a1=8a1=8 and the last term as an=26an=26.
The formula to find the nth term of an A.P. is an=a1+(n−1)⋅dan=a1+(n−1)⋅d.
Given an=26an=26 and a1=8a1=8, we can find the common difference (d).
26=8+(n−1)⋅d26=8+(n−1)⋅d
18=(n−1)⋅d18=(n−1)⋅d
Now, let's choose a value for nn, say n=6n=6 (because we need to insert 5 numbers between 8 and 26).
18=(6−1)⋅d18=(6−1)⋅d 18=5d18=5d d=185=3.6d=518=3.6
Now, we can find the numbers by adding the common difference to each preceding term.
a2=a1+d=8+3.6=11.6a2=a1+d=8+3.6=11.6 a3=a2+d=11.6+3.6=15.2a3=a2+d=11.6+3.6=15.2 a4=a3+d=15.2+3.6=18.8a4=a3+d=15.2+3.6=18.8 a5=a4+d=18.8+3.6=22.4a5=a4+d=18.8+3.6=22.4 a6=a5+d=22.4+3.6=26a6=a5+d=22.4+3.6=26
So, the resulting sequence forming an A.P. with 5 numbers inserted between 8 and 26 is:
8,11.6,15.2,18.8,22.4,268,11.6,15.2,18.8,22.4,26
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