Here, we are required to find the first term of an arithmetic progression which has a second term of 96 and a fourth term of 54.
- The first term of the progression which has a <em>second term</em> of 96 and a <em>fourth term</em> of 54 is; a = 117.
<em>In Arithmetic progression, the N(th) term of the progression is given by the formular;</em>
T(n) = a + (n-1)d
where;
Therefore, from the question above;
- T(2nd) = a + d = 96..............eqn(1)
- and T(4th) = a + 3d = 54..........eqn(2)
By solving the system of equations simultaneously;
we subtract eqn. 2 from 1, then we have;
<em>-2d = 42</em>
Therefore, d = -21.
However, the question requests that we find the first term of the progression; From eqn. (1);
a + d = 96
Therefore,
Ultimately, the first term of the progression is therefore; a = 117
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For a, we have 42in/9ft. Since 12 inches are in 1 foot, we can multiply it by that to get (42in/9ft)*(1ft/12inches) = 42/108. We put the foot on the top of 1ft/12in to cancel them out. Since 2 goes into both 42 and 108, we divide it by 2/2 to get 26/54. Repeating the process again, we get 13/27
If we were to say that there are 12 inches in a foot and therefore divide 42 by 12 (to get 42 inches in feet), we'd get the same answer due to that 1 foot is equal to 12 inches and if you were to divide it by 1 foot/12 inches, since they are the same thing, you get the same answer
For c, since it may be hard to get (42/12)/9, it could just be easier to have 42/(9*12)=42/108
Answer:
the answer would be 169.666666667
