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Find the term of the geometric sequence. 4,12,36,108,dots r=c Find the 6 th term.

2323. Find the term of the geometric sequence.\newline4,12,36,108,… 4,12,36,108, \ldots \newliner=c r=c \newlineFind the 66 th term.

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Q. 2323. Find the term of the geometric sequence.\newline4,12,36,108,… 4,12,36,108, \ldots \newliner=c r=c \newlineFind the 66 th term.
  1. Identify common ratio: Identify the common ratio rr of the geometric sequence.\newlineThe sequence is 4,12,36,108,…4, 12, 36, 108, \dots\newlineTo find the common ratio, divide the second term by the first term.\newliner=124=3r = \frac{12}{4} = 3
  2. Find 66th term: Use the common ratio to find the 66th term.\newlineThe nth term of a geometric sequence is given by the formula:\newlineTn=a⋅r(n−1)T_n = a \cdot r^{(n-1)}\newlinewhere TnT_n is the nth term, aa is the first term, and rr is the common ratio.\newlineFor the 66th term (T6T_6), a=4a = 4, r=3r = 3, and n=6n = 6.\newlineT6=4⋅3(6−1)=4⋅35T_6 = 4 \cdot 3^{(6-1)} = 4 \cdot 3^5
  3. Calculate value: Calculate 353^5 to find the value of T6T_6. \newline35=3×3×3×3×3=2433^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243\newlineNow, multiply this by the first term (a=4a = 4).\newlineT6=4×243=972T_6 = 4 \times 243 = 972

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