Math, asked by abrahmanf10, 8 hours ago

In an AP if Sn = n2+2n, its 18th term is
pls answer fast

Answers

Answered by user0888
6

Solution

Assuming S_{n} as a sum of an arithmetic progression \{a_{n}\},

by definition,

\implies S_{n}=a_{1}+a_{2}+...+a_{n-1}+a_{n}\ \ \ \ \ (1)

\implies S_{n-1}=a_{1}+a_{2}+...+a_{n-1}\ \ \ \ \ (2)

By (1) and (2),

\implies S_{n}-S_{n-1}=a_{n}\ (n\geq 2)

\implies a_{n}=(n^{2}+2n)-\{(n-1)^{2}+2(n-1)\}\ (n\geq 2)

\implies a_{n}=2n+1\ (n\geq 2)

The required value is,

\implies a_{18}

So the answer is,

\implies \boxed{37}

Learn more

S_{n} having a constant term does not give an A.P when n=1, for example,

\implies S_{n}=2n^{2}+3n+1

\implies S_{n}-S_{n-1}=(2n^{2}+3n+1)-\{2(n-1)^{2}+3(n-1)+1\}

\implies a_{n}=4n+1\ (n\geq 2)

But, we see that,

\implies a_{1}=6

This means,

\implies a_{1}\neq 4n+1

Now we have two cases.

When n=1, by definition,

\implies S_{1}=a_{1}

When n\geq 2, by definition,

\implies S_{n}-S_{n-1}=a_{n}

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