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For an arithmetic progression where \( a = 25 \) and \( d = 100 \), find the first four terms and the formula for the nth term.

A. 25, 125, 225, 325; \( T_n = 25 + 100(n - 1) \)

B. 25, 125, 225, 325; \( T_n = 25 + 100n \)

C. 25, 100, 225, 400; \( T_n = 25 + 100(n - 1) \)

D. 25, 100, 225, 400; \( T_n = 25 + 100n \)

Answer :

Final answer:

Option (A), The first four terms of the arithmetic progression with a first term of 25 and a common difference of 100 are 25, 125, 225, 325. The formula for the nth term of this arithmetic sequence is Tn = 25 + 100(n - 1).

Explanation:

The question asks for the first four terms and the formula for the nth term of an arithmetic progression, given that the first term (a) is 25 and the common difference (d) is 100. In an arithmetic progression, each term after the first is obtained by adding a constant difference to the previous term. Thus, the first four terms of the sequence are given by:

  1. First term: a = 25
  2. Second term: a + d = 25 + 100 = 125
  3. Third term: a + 2d = 25 + 2*100 = 225
  4. Fourth term: a + 3d = 25 + 3*100 = 325

The general formula for the nth term of an arithmetic sequence is given by Tn = a + (n - 1)d. Hence, the formula for the nth term of this sequence is Tn = 25 + 100(n - 1).

The answer is, therefore, option (a): 25, 125, 225, 325; Tn = 25 + 100(n - 1).

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