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c(n)=-(9)/(2)(-(4)/(3))^(n-1) What is the 2^("nd ") term in the sequence?

c(n)=−92(−43)n−1 c(n)=-\frac{9}{2}\left(-\frac{4}{3}\right)^{n-1} \newlineWhat is the 2nd  2^{\text {nd }} term in the sequence?

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Full solution

Q. c(n)=−92(−43)n−1 c(n)=-\frac{9}{2}\left(-\frac{4}{3}\right)^{n-1} \newlineWhat is the 2nd  2^{\text {nd }} 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 c(n)=−92(−43)n−1c(n)=-\frac{9}{2}\left(-\frac{4}{3}\right)^{n-1}. We need to find the second term, which means we will substitute nn with 22 in the formula.
  2. Step 22: Substitute n n with 2 2 : Substitute n n with 2 2 in the sequence formula.c(2)=−92(−43)2−1 c(2) = -\frac{9}{2}\left(-\frac{4}{3}\right)^{2-1}
  3. Step 33: Simplify the exponent: Simplify the exponent.\newlineSince 2−12^{-1} equals 11, the expression becomes:\newlinec(2)=−92(−43)1c(2)=-\frac{9}{2}\left(-\frac{4}{3}\right)^1
  4. Step 44: Calculate the value of the term: Calculate the value of the term with the exponent applied.\newlineThe expression simplifies to:\newlinec(2)=−92(−43)c(2)=-\frac{9}{2}\left(-\frac{4}{3}\right)
  5. Step 55: Multiply the constants: Multiply the constants.\newlineNow we multiply −(92)-(\frac{9}{2}) by (−43)(-\frac{4}{3}):\newlinec(2)=−(92)×(−43)c(2)=-(\frac{9}{2}) \times (-\frac{4}{3})\newlinec(2)=9×42×3c(2)= \frac{9 \times 4}{2 \times 3}\newlinec(2)=366c(2)= \frac{36}{6}
  6. Step 66: Simplify the fraction: Simplify the fraction to find the second term. c(2)=366c(2)= \frac{36}{6} equals 66.

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