Question

A geometric sequence h starts with 10, 5, . . . Explain how you would calculate the value of the 100th term.

Answer 1

The 100th term of the sequence is 1.57 × 10^29

The nth term of an arithmetic progression is expressed using the formula:

Tn = $ar^{n-1}$

• a is the first term

• r is the common ratio

• n is the number of terms'

Given the sequence:

10, 5...

a = 10

r = 5/10 = 1/2

Since we need the 100th term, n = 100

Substitute the given parameter into the formula:

$T_{100} = 10(1/2)^{100-1}\\T_{100}= 10*0.5^{99}\\T_{100}=10 \times 1.57\times 10^{-30}\\T_{100} = 1.57\times 10^{29}$

Hence the 100th term of the sequence is 1.57 × 10^29

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