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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