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In an arithmetic sequence, the first term, 
a_(1), is equal to 9 , and the sixth term, 
a_(6), is equal to 24 . Which number represents the common difference of the arithmetic sequence?

d=2

d=3

d=4

d=5

In an arithmetic sequence, the first term, a1 a_{1} , is equal to 99 , and the sixth term, a6 a_{6} , is equal to 2424 . Which number represents the common difference of the arithmetic sequence?\newlined=2 d=2 \newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5

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Q. In an arithmetic sequence, the first term, a1 a_{1} , is equal to 99 , and the sixth term, a6 a_{6} , is equal to 2424 . Which number represents the common difference of the arithmetic sequence?\newlined=2 d=2 \newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5
  1. Given Terms: We are given the first term a1a_1 and the sixth term a6a_6 of an arithmetic sequence. The first term a1a_1 is 99, and the sixth term a6a_6 is 2424. We need to find the common difference dd.
  2. Arithmetic Sequence Formula: The formula for the nnth term of an arithmetic sequence is an=a1+(n1)da_n = a_1 + (n - 1)d, where a1a_1 is the first term, dd is the common difference, and nn is the term number.
  3. Express Sixth Term: We can use the formula to express the sixth term: a6=a1+(61)d=a1+5da_6 = a_1 + (6 - 1)d = a_1 + 5d.
  4. Substitute Values: Substitute the given values into the equation: 24=9+5d24 = 9 + 5d.
  5. Solve for d: Solve for d: 24=9+5d24 = 9 + 5d implies 249=5d24 - 9 = 5d, which simplifies to 15=5d15 = 5d.
  6. Divide by 55: Divide both sides by 55 to find dd: d=155d = \frac{15}{5}.
  7. Calculate d: Calculate the value of d: d=3d = 3.

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