Answer :
The first term of a sequence is -87. 165 is 37th term of given Arithmetic sequence.
Solution:
Given that ;
First term of the sequence [tex]a_{1} = -87[/tex]
Also each successive term is created by adding 7 to its previous term. This means given sequence is an arithmetic sequence with common difference d = 7.
Let’s say 165 be [tex]n^{th}[/tex] term of above arithmetic sequence that is [tex]a_{n}[/tex] = 165. We need to determine n.
Formula of [tex]n^{th}[/tex] term of arithmetic sequence is as follows:
[tex]\mathrm{a}_{\mathrm{n}}=\mathrm{a}_{1}+(\mathrm{n}-1) \mathrm{d}[/tex]
where [tex]a_{1}[/tex] is the first term of the sequence
"d" is the common difference ratio
Substituting the given values we get
165 = -87 + (n-1) 7
165 + 87 = 7n – 7
7n = 165 + 87 + 7
n = [tex]\frac{259}{7}[/tex] = 37
Hence 165 is 37th term of given Arithmetic sequence.
