Q. Find the 10th term of the geometric sequence shown below.x4,5x6,25x8,…Answer:
Identify common ratio: Identify the common ratio (r) of the geometric sequence by dividing the second term by the first term.Calculation: r=x45x6=5x6−4=5x2
Use nth term formula: Use the formula for the nth term of a geometric sequence, which is an=a1⋅r(n−1), where a1 is the first term and n is the term number.Calculation: The first term a1 is x4, the common ratio r is 5x2, and the term number n is 10.
Substitute values: Substitute the values into the formula to find the 10th term.Calculation: a10=x4⋅(5x2)10−1=x4⋅(5x2)9
Simplify expression: Simplify the expression by raising the common ratio to the 9th power.Calculation: (5x2)9=59⋅(x2)9=59⋅x18
Multiply terms: Multiply the first term x4 by the simplified common ratio 59⋅x18.Calculation: a10=x4⋅59⋅x18
Combine like terms: Combine the like terms by adding the exponents of x.Calculation: a10=59⋅x4+18=59⋅x22
Calculate coefficient: Calculate the value of 59 to get the coefficient of x22.Calculation: 59=1953125
Write final expression: Write the final expression for the 10th term.Calculation: a10=1953125⋅x22
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