Question

The first term of a geometric sequence is 4 and grows exponentially by a factor of 3. Murphy writes out the terms and says that the sum of the 4th and 5th terms is​ 1,296. Explain​ Murphy's error and correct it. (Fill in the blanks)
Murphy added terms
____
together. The correct sum of the 4th and 5th terms is ___
​(Simplify your​ answer.)

Answer 1

The geometric sequence can increase or decrease exponentially

The correct sum of the 4th and the 5th terms is 432

How to determine the correct sum?

The given parameters are:

Initial value (a) = 4

Growth factor (r) = 3

The nth term of a geometric sequence is calculated as:

$T_n = ar^{n-1}$

This gives

$T_n = 4 * 3^{n-1}$

For the 4th term; we have:

$T_4 = 4 * 3^{4-1}$

$T_4 = 108$

For the 5th term, we have:

$T_5 = 4 * 3^{5-1}$

$T_5 = 324$

Add the 4th and the 5th terms

Sum = 108 + 324

Sum = 432

Hence, the correct sum of the 4th and the 5th terms is 432

Read more about geometric sequence at:

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