If 6 arithmetic means are inserted between 1 and 29, then find the 4th arithmetic mean.

Let a1,a2,a3,a4,a5,a6 be sic arithmetic means⇒1,a1,a2,.....,a6,9/2 will be in A.P.Now,nth term an=a+(n−1)d8th term 29=1+7d⇒27=7d⇒d=21.Hence 4th term a4=1+4(21)=3.

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If 6 arithmetic means are inserted between 1 and 92, then fin

Question

If $6$ arithmetic means are inserted between $1$ and $\frac{9}{2}$ , then find the $4^{t h}$ arithmetic mean.

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6

arithmetic means are inserted between

1

and

\frac{9}{2}

, then find the

4^{t h}

arithmetic mean.

7 mins ago

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7 mins ago

Text solutionVerified

Let

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}

be sic arithmetic means

\Rightarrow 1, a_{1}, a_{2}, ....., a_{6}, 9/2

will be in A.P.

Now,

n^{t h}

term

a_{n} = a + (n - 1) d

8^{t h}

term

\frac{9}{2} = 1 + 7 d \Rightarrow \frac{7}{2} = 7 d \Rightarrow d = \frac{1}{2}

Hence

4^{t h}

term

a_{4} = 1 + 4 (\frac{1}{2}) = 3

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Question Text	If $6$ arithmetic means are inserted between $1$ and $\frac{9}{2}$ , then find the $4^{t h}$ arithmetic mean.
Answer Type	Text solution:1
Upvotes	150

If 6 arithmetic means are inserted between 1 and 29​, then find the 4th arithmetic mean.

Text solutionVerified

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If $6$ arithmetic means are inserted between $1$ and $\frac{9}{2}$ , then find the $4^{t h}$ arithmetic mean.