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 second term of 96 and a fourth term of 54 is; a = 117.
In Arithmetic progression, the N(th) term of the progression is given by the formular;
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;
-2d = 42
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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