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In a geometric sequence, the first term, 
a_(1), is equal to 1 , and the fourth term, 
a_(4), is equal to 27 . Which number represents the common ratio of the geometric sequence?

r=1

r=2

r=3

r=4

In a geometric sequence, the first term, a1 a_{1} , is equal to 11 , and the fourth term, a4 a_{4} , is equal to 2727 . Which number represents the common ratio of the geometric sequence?\newliner=1 r=1 \newliner=2 r=2 \newliner=3 r=3 \newliner=4 r=4

Full solution

Q. In a geometric sequence, the first term, a1 a_{1} , is equal to 11 , and the fourth term, a4 a_{4} , is equal to 2727 . Which number represents the common ratio of the geometric sequence?\newliner=1 r=1 \newliner=2 r=2 \newliner=3 r=3 \newliner=4 r=4
  1. Identify Given Terms: Identify the given terms in the geometric sequence. We are given the first term a1=1a_1 = 1 and the fourth term a4=27a_4 = 27.
  2. Use Formula for nth Term: Use the formula for the nth term of a geometric sequence to find the common ratio.\newlineThe formula for the nth term of a geometric sequence is an=a1r(n1)a_n = a_1 \cdot r^{(n-1)}, where rr is the common ratio.
  3. Substitute Given Terms: Substitute the given terms into the formula to create an equation.\newlineWe know that a4=a1×r41a_{4} = a_{1} \times r^{4-1}, which simplifies to 27=1×r327 = 1 \times r^3.
  4. Solve for Common Ratio: Solve for the common ratio rr. Since 27=r327 = r^3, we can find rr by taking the cube root of 2727. r=271/3r = 27^{1/3} r=3r = 3

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