Find the 12th term of an AP of the form 7, 12, 17, 22

Mathematics

1 answer:

Nostrana [21]2 years ago

6 0

Answer:

Step-by-step explanation:

The rule will be

Ni=(i-1)*5+2

i=1 → N=(1–1)*5+2=0*5+2=0+2=2
i=2 → N=(2–1)*5+2=1*5+2=5+2=7
i=3 → N=(3–1)*5+2=2*5+2=10+2=12
i=4 → N=(4–1)*5+2=3*5+2=15+2=17
i=5 → N=(5–1)*5+2=4*5+2=20+2=22
i=6 → N=(6–1)*5+2=5*5+2=25+2=27

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An arithmetic sequence with a thrid term of 8 and constant difference of 5

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$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
d=5\\
a_3=8\\
n=3
\end{cases}
\\\\\\
a_3=a_1+(3-1)5\implies 8=a_1+(2)5\implies 8=a_1+10
\\\\\\
\boxed{-2=a_1}
\\\\\\
a_n=-2+(n-1)5$