Question

In an arithmetic sequence, the sum of the 2nd and 6th terms is 32. Given that the sum of the first six terms is 120, find the common difference of the sequence.

a) 4
b) 5
c) 6
d) 7

Answer 1

The correct common difference of the arithmetic sequence is 5. Option B is answer.

Step-by-step explanation:

Let "a" be the first term, and "d" be the common difference of the arithmetic sequence.

The 2nd term is "a + d," and the 6th term is "a + 5d."

According to the given information, "(a + d) + (a + 5d) = 32."

Combine like terms: "2a + 6d = 32."

The sum of the first six terms is "6a + 15d = 120" (given).

Substitute "a = (32 - 6d)/2" into the second equation.

Solve the system of equations to find "d = 5."

Therefore, the common difference of the arithmetic sequence is 5.

Option B is answer.