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If a(n)={(1+(-1)^(n))/23^(n)} then a(7)=...

If `a_(n)={(1+(-1)^(n))/23^(n)}` then `a_(7)=`……………………

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To solve the problem where \( a_n = \frac{1 + (-1)^n}{23^n} \) and we need to find \( a_7 \), we can follow these steps: ### Step 1: Substitute \( n = 7 \) into the formula We start by substituting \( n = 7 \) into the expression for \( a_n \). \[ a_7 = \frac{1 + (-1)^7}{23^7} \] ### Step 2: Calculate \( (-1)^7 \) Next, we need to evaluate \( (-1)^7 \). Since 7 is an odd number, we have: \[ (-1)^7 = -1 \] ### Step 3: Substitute back into the equation Now we substitute \( (-1)^7 \) back into the equation for \( a_7 \): \[ a_7 = \frac{1 + (-1)}{23^7} \] ### Step 4: Simplify the numerator Now we simplify the numerator: \[ 1 + (-1) = 0 \] So, we have: \[ a_7 = \frac{0}{23^7} \] ### Step 5: Calculate the final result Since the numerator is 0, the entire fraction becomes: \[ a_7 = 0 \] Thus, the final answer is: \[ \boxed{0} \] ---
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