The sum of 14 terms of the arithmetic sequence having the first term, a₁ = 18, and the constant difference, d = 9.4 is given as S₁₄ = 1107.4. Hence, the first option is the right choice.
An arithmetic sequence is a special sequence where every term is the sum of the previous term and a constant.
The sum of an arithmetic sequence having n-terms, with the first term being a, and the constant difference being d is given by the formula:
Sₙ = (n/2){2a + (n - 1)d}, where Sₙ is the sum of n-terms.
In the question, we are asked to find the sum of 14 terms for the arithmetic sequence, where the first term, a₁ = 18, and the constant difference, d = 9.4.
We know that the sum of an arithmetic sequence having n-terms, with the first term being a, and the constant difference being d is given by the formula:
Sₙ = (n/2){2a + (n - 1)d}, where Sₙ is the sum of n-terms.
Thus, substituting n = 14, a = 18, and d = 9.4 in the above formula, we get:
S₁₄ = (14/2){2(18) + (14 - 1)(9.4)},
or, S₁₄ = 7{36 + 122.2},
or, S₁₄ = 7*158.2,
or, S₁₄ = 1107.4.
Thus, the sum of 14 terms of the arithmetic sequence having the first term, a₁ = 18, and the constant difference, d = 9.4 is given as S₁₄ = 1107.4. Hence, the first option is the right choice.
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