Question

Find the eighth term of the geometric sequence which the third term is 36 and the fifth term is 81 .​

Answer 1

Answer:

The nth term of a geometric sequence is given by

an = am×rn−m where:r = common ratio

Use the formula above to solve for r .

an = am×rn−m

a5 = a3×r5–3

a5 = a3×r2

81 = 36×r2

2.25 = r2

r = 1.5

Use again the formula to solve for the 8th term.

an = am×rn−m

a8 = a5×r8–5

a8 = 81×1.53

a8 = 81×1.53 = 273.375

Step-by-step explanation:

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Answer 2

Given: The third term of a geometric sequence is 36 and the fifth term is 81.

To find:  The eighth term of the geometric sequence.

Solution:

• A term in a geometric sequence is given by the formula,

       $T_{n} = a r^{n-1}$

• Here, the $n^{th}$ is to be found, a is the first term of the geometric sequence and r is the common ratio of the sequence.
• According to the given question,

       $ar^{2} = 36$

       $ar^{4} = 81$

• On dividing the above two equations, the values of a and r are found to be,

        $a = 16$ and $r = \frac{3}{2}$

• In order to find the eighth term, the following calculations are made,

        $ar^{7} = 16 * (\frac{3}{2})^{7}$

              $= 273.375$

Therefore, the eighth term of the geometric sequence is 273.375.