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a(n)=(3)/(2)(-2)^(n-1) What is the 3^("rd ") term in the sequence?

a(n)=32(−2)n−1 a(n)=\frac{3}{2}(-2)^{n-1} \newlineWhat is the 3rd  3^{\text {rd }} term in the sequence?

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Full solution

Q. a(n)=32(−2)n−1 a(n)=\frac{3}{2}(-2)^{n-1} \newlineWhat is the 3rd  3^{\text {rd }} term in the sequence?
  1. Step 11: Understand sequence formula: Understand the sequence formula and identify the term to find.\newlineThe sequence is defined by the formula a(n)=32(−2)n−1a(n)=\frac{3}{2}(-2)^{n-1}. We need to find the 3rd3^{\text{rd}} term, which means we will substitute nn with 33 in the formula.
  2. Step 22: Substitute n n with 3 3 : Substitute n n with 3 3 in the sequence formula.a(3)=32(−2)3−1a(3)=\frac{3}{2}(-2)^{3-1}
  3. Step 33: Calculate the exponent: Calculate the exponent part of the formula. (−2)(3−1)=(−2)2(-2)^{(3-1)} = (-2)^2
  4. Step 44: Evaluate the exponent: Evaluate the exponent.\newline(−2)2=4(-2)^2 = 4
  5. Step 55: Multiply by the coefficient: Multiply the result of the exponentiation by the coefficient.\newline(32)×4=3×2=6(\frac{3}{2}) \times 4 = 3 \times 2 = 6
  6. Step 66: Final answer: Write down the final answer.\newlineThe 3rd3^{\text{rd}} term in the sequence is 66.

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