Final answer:
The sum of the first ten terms of the arithmetic sequence with a first term of 1 and a common difference of 1.4 should be 73, using the formula for the sum of an arithmetic sequence. However, the options provided do not match this result, and if we consider the sequence without the common difference (simply 1 to 10), the sum would be 55.
Step-by-step explanation:
The question involves determining the sum of the first ten terms of an arithmetic sequence. An arithmetic sequence starts with a first term of '1' and with a common difference of '1.4', per the given pattern. To find the sum of the first ten terms (S10), we can use the formula for the sum of an arithmetic sequence: Sn = n/2 × (2a + (n-1)d), where 'n' is the number of terms, 'a' is the first term, and 'd' is the common difference.
Applying this formula, S10 = 10/2 × (2 × 1 + (10-1) × 1.4) gives us S10 = 5 × (2 + 9 × 1.4) = 5 × (2 + 12.6) = 5 × 14.6, thus S10 = 73. So, the correct answer is neither of the options provided, suggesting there might be a misunderstanding or typo in the question.
If we ignore the common difference and consider the sequence to be simply the integers from 1 to 10, then S10 would be 55, using the formula for the sum of the first n integers: Sn = n/2 × (a + l), where 'l' is the last term, which would match option A).