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A progression has a second term of 96 and a fourth term of 54. Find the first term of the progression of the progression is arithmetic.

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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;

  • a = first term

  • d = common difference.

  • n = nth term.

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,

  • a - 21 = 96
  • a = 96 + 21

Ultimately, the first term of the progression is therefore; a = 117

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