Find the indicated term of each arithmetic sequence.
37th term: [tex]a(1) = -3[/tex]; [tex]d = 2.8[/tex]
Answer (2)
In an arithmetic sequence, a certain amount is added every time to reach the next value. * eg* 3,6,9,12
Each time, ** 3** is added to reach the next value.
So starting from the original value (a), and given the amount it increases by (d), we can calculate the value of any term in an arithmetic sequence.
For a given term in an arithmetic sequence, it's value can be expressed as:
u n = a + ( n − 1 ) d
Substituting in the values you have given ( a = − 3 , d = 2.8 ) , we get:
u 37 = − 3 + ( 37 − 1 ) 2.8 u 37 = 100.8 − 2 u 3 7 = 97.8
The 37th term of the arithmetic sequence is found using the formula u n = a + ( n − 1 ) d . After calculating with the given values a = − 3 and d = 2.8 , the result is 97.8. Thus, the 37th term is 97.8.
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