Maintaining Mathematical Proficiency
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What is the first term of the sequence? What is the common difference between terms? Use these values in the explicit equation for arithmetic sequences.
Equation: a_n=17n-46
Value of a_(50): 804
Explicit equations for arithmetic sequences follow a specific format.
a_n= a_1+( n-1) d
In this form, a_1 is the first term in a given sequence, d is the common difference from one term to the next, and a_n is the nth term in the sequence. For this exercise, the first term is a_1= - 29. Let's observe the other terms to determine the common difference d.
d= 17, a_1= - 29
Distribute 17
Subtract term
This equation can be used to find any term in the given sequence. To find a_(50), the 50th term in the sequence, we substitute 50 for n.
n= 50
Multiply
Subtract term
The 50th term in the sequence is 804.