Question

2 + 5 + 8 + 11 + 14

Use the arithmetic explicit formula to find n for the number 14 in the sequence. Use the formula.
Write the arithmetic sum formula.

Answer 1

Explanation:

the difference is 3 a is is first term which is 2

the formula is sn= a+(n-1)d

2+(n-1)3

2+(3n-3)

Answer 2

The sum of the sequence is 40.

Explanation:

The given sequence is an arithmetic sequence with a common difference of 3. To find the value of n for the number 14 in the sequence, we can use the explicit formula for an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_n is the nth term of the sequence, a_1 is the first term, d is the common difference, and n is the term number.

Substituting the given values, we get:

14 = 2 + (n-1)3

Simplifying the equation, we get:

12 = 3n - 3

15 = 3n

n = 5

Therefore, the number 14 appears as the 5th term in the sequence.

To find the sum of the sequence, we can use the arithmetic sum formula:

S_n = (n/2)(a_1 + a_n)

where S_n is the sum of the first n terms of the sequence.

Substituting the given values, we get:

S_5 = (5/2)(2 + 14)

S_5 = 40

Therefore, the sum of the sequence is 40.