Question

Find the 10th term of the geometric sequence whose common ratio is 1/2 and whose first term is 7 .

Answer 1

• 7/512

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Use the formula for nth term of a GP:

• tₙ = a * rⁿ⁻¹,

where,

• tₙ is the nth term of the sequence,
• a is the first term of the sequence, and
• r is the common ratio.

In this case:

• the first term a = 7 and
• the common ratio r = 1/2.

So, to find the 10th term, we substitute the values into the formula:

• t₁₀ = 7 * (1/2)¹⁰⁻¹

Simplifying the exponent:

• t₁₀ = 7 * (1/2)⁹
• t₁₀ = 7 * (1/512)
• t₁₀ = 7/512