In Problems 17 − 24 , find the n th term of the arithmetic sequence { a n } whose first term a 1 and common difference d are given. What is the 51 st term? a 1 = 8 ; d = − 7
In Problems 17 − 24 , find the n th term of the arithmetic sequence { a n } whose first term a 1 and common difference d are given. What is the 51 st term? a 1 = 8 ; d = − 7
In Problems
17
−
24
, find the
n
th term of the arithmetic sequence
{
a
n
}
whose first term
a
1
and common difference
d
are given. What is the
51
st term?
a
1
=
8
;
d
=
−
7
Expert Solution & Answer
To determine
The nth and then 51st term of the arithmetic sequence whose first term a1=8 and the common difference d=−7.
Answer to Problem 17AYU
Solution:
The nth term an=−7n+15 and the 51st term of the arithmetic sequence is −342.
Explanation of Solution
Given information:
The first term of the arithmetic sequence is a1=8, and common difference is d=−7.
Explanation:
The nth term of the arithmetic sequence is determined by the formula
an=a1+(n−1)d.
Substituting a1=8 and d=−7,
an=8+(n−1)(−7),
By simplifying,
an=8−7n+7=−7n+15
Thus, the nth term of the sequence is an=−7n+15.
To find the 51st term, substitute n=51 in the above formula
Therefore, 51st term is a51=−7(51)+15=−342
Thus, the 51th term of arithmetic sequence is −342.
Thomas' Calculus: Early Transcendentals (14th Edition)
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