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McGraw Hill Glencoe Algebra 1, 2012 – Analyzing Functions with Successive Differences

Equation: a_n=-20(0.5)^(n-1)
Value of a_7: -0.3125

Solution

Explicit equations for geometric sequence follow a specific format. a_n= a_1 r^(n-1) In this form, a_1 is the first term in a given sequence, r is the common ratio from one term to the next, and a_n is the {\color{#FF0000}{n}}^\text{th} term in the sequence. For this exercise, the first term is a_1= - 20. Let's observe the other terms to determine the common ratio r. -20* 0.5 →- 10* 0.5 →- 5 ... By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.

a_n=a_1r^(n-1)
SubstituteII

r= 0.5, a_1= -20

a_n= - 20( 0.5)^(n-1)

This equation can be used to find any term in the given sequence. To find a_7, the {\color{#FF0000}{7}}^\text{th} term in the sequence, we substitute 7 for n.

a_n=-20(0.5)^(n-1)
Substitute

n= 7

a_7=-20(0.5)^(7-1)
SubTerm

Subtract term

a_7=-20(0.5)^6
CalcPow

Calculate power

a_7=-20(0.015625)
Multiply

Multiply

-0.3125

The 7^\text{th} term in the sequence is -0.3125.

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