Question

Writing the formula of sequences calculator.

A. S_n = a + (n-1)d
B. S_n = \frac{n}{2}[2a + (n-1)d]
C. S_n = a \times r^{(n-1)}
D. S_n = \frac{n}{2}(a + l)

Answer 1

The student's question involves finding the correct formula to calculate the sum of a sequence, which is Formula B: S_n = \frac{n}{2}[2a + (n-1)d], the sum of the first n terms of an arithmetic sequence.

Step-by-step explanation:

The student's question seems to revolve around the correct formula for calculating the sum of a sequence. This topic falls under high school mathematics, specifically within the field of series and sequences. To answer the student's question:

• Formula A. S_n = a + (n-1)d is the formula for the nth term of an arithmetic sequence, not the sum.
• Formula B. S_n = \frac{n}{2}[2a + (n-1)d] is the correct formula for the sum of the first n terms of an arithmetic sequence.
• Formula C. S_n = a \times r^{(n-1)} represents the nth term of a geometric sequence, not the sum.
• Formula D. S_n = \frac{n}{2}(a + l) is another form of the formula for the sum of an arithmetic sequence, where 'a' is the first term and 'l' is the last term.

The binomial theorem and other details provided in the question are not directly relevant to finding the sum of an arithmetic sequence, as they pertain to series expansions and other mathematical concepts.