What Is The Number Of Terms In The Sequence 7, 10, 13, … , 35
What is the number of terms in the sequence 7, 10, 13, … , 35
[tex]\tt{\huge{\blue{Explanation:}}}[/tex]
The nth term of an arithmetic sequence is
[tex]\boxed{a_{n} = a_{1} + (n – 1)(d)}[/tex]
where:
aₙ = nth term
a₁ = first term
n = number of terms
d = common difference
[tex]\tt{\huge{\red{Solution:}}}[/tex]
Solving for the common difference
[tex]d = a_{2} – a_{1}[/tex]
[tex]d = 10 – 7[/tex]
[tex]d = 3[/tex]
Solving for the number of terms
[tex]a_{n} = a_{1} + (n – 1)(d)[/tex]
[tex]25 = 7 + (n – 1)(3)[/tex]
[tex]3(n – 1) = 25 – 7[/tex]
[tex]3(n – 1) = 18[/tex]
[tex](n – 1) = 6[/tex]
[tex]n = 6 + 1[/tex]
[tex]\boxed{n = 7}[/tex]
Therefore, the number of terms is 7.
[tex]\\[/tex]
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