Answered

9) 32, 42, 52, 62, ...
A) Common Difference: d = 10
a = 550
52
B) Common Difference: d = 10
a = 542
a52
52
C) Common Difference: d = 10
a = 560
52
D) Common Difference: d = 10
a = 540
52



Answer :

The given sequence is 32, 42, 52, 62, and we are to determine the common difference and identify the correct term.

In an arithmetic sequence, each term increases by a constant value known as the common difference. For this sequence:

  1. The first term (a1) is 32.
  2. The second term (a2) is 42.
  3. The third term (a3) is 52.
  4. The fourth term (a4) is 62.

To find the common difference (d), subtract the first term from the second term:

d = 42 - 32 = 10

Thus, the common difference is 10.

The required nth term of an arithmetic sequence is given by the formula: an = a1 + (n-1)d.

Given options focus on determining the correct term:

  • an = 32 + (n-1)10
  • an = 32 + 10(n - 1)

Find the common difference in the sequence.

Question: 32, 42, 52, 62, ... Determine the common difference.

Step-by-step Explanation:

  1. Subtract each number from the one following it to identify the differences: 42-32 = 10, 52-42 = 10, 62-52 = 10.
  2. Since the differences are consistent at 10, the common difference is 10.
  3. The answer should be: Common Difference: d = 10.

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