Question

The arithmetic mean of the numbers 7, 14, 21, ..., 63 is

• A. 38
• B. 37
• C. 36
• D. 35

Hint:

For equally spaced numbers, mean = (first term + last term) / 2.

Answer 1

The Correct Option is D

To find the arithmetic mean of the numbers in the sequence 7, 14, 21, ..., 63, we follow these steps:

1. Identify the given sequence: This is an arithmetic sequence where the first term \(a = 7\), and the last term \(l = 63\). The common difference \(d = 14 - 7 = 7\).
2. Find the number of terms in the sequence:
   • Use the formula for the n-th term of an arithmetic sequence: \(l = a + (n-1)d\).
   • Substitute the known values: \(63 = 7 + (n-1) \times 7\).
   • Solve for n:
     • \(63 = 7 + 7(n-1)\)
     • \(63 = 7 + 7n - 7\)
     • \(63 = 7n\)
     • \(n = \frac{63}{7} = 9\)
3. Calculate the arithmetic mean:
   • The formula for the arithmetic mean M of an arithmetic sequence is \(M = \frac{a + l}{2}\).
   • Substitute the values: \(M = \frac{7 + 63}{2}\).
   • \(M = \frac{70}{2} = 35\)

Therefore, the arithmetic mean of the numbers in this sequence is 35.