In general- the numbers 1a-1a-d-1a - 2d-1a- n-1d are in

The correct option is D H.P.The reciprocal of the given numbers is #160; a, a+d, a+2d, .......,a+(n 1)d which is an AP with common difference d So, t ...

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Byju's Answer

Standard X

Mathematics

Formula for Sum of n Terms of an AP

In general, t...

Question

In general, the numbers $\frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . . . ., \frac{1}{a + (n - 1) d}$ are in

G.P.

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A.P.

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I.P.

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H.P.

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Solution

The correct option is D H.P.
The reciprocal of the given numbers is $a, a + d, a + 2 d, . . . . . . ., a + (n - 1) d$
which is an AP with common difference $d$
So, the given numbers $\frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . . . \frac{1}{a + (n - 1) d}$ are in HP.

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Similar questions

$a + (a + d) + (a + 2 d) + . . . . + (a + (n - 1) d) = \frac{n}{2} [2 a + (n - 1) d]$

Q. a+(a+d) +(a+2d) + ...... +(a+(n-1)d)= 1/2 n× {2a+(n-1)d}, n belongs to N

Q. If

θ = t a n^{- 1} \frac{d}{1 + a_{1} a_{2}} + t a n^{- 1} \frac{d}{1 + a_{2} a_{3}} + \dots + t a n^{- 1} \frac{d}{1 + a_{n - 1} a_{n}}

, where

a_{1}, a_{2}, a_{3}, \dots a_{n}

are in A.P. with common difference d, then

t a n θ =

Q. If

\frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . .

are in HP, then the

n^{t h}

term of the HP is

Q. In the series

a + (a + d) r + (a + 2 d) r^{2} + . . . . (a + ¯ ¯¯¯¯¯¯¯¯¯¯¯ ¯ n - 1 . d) r^{n - 1}

. Find the sum if

r < 1

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In general, the numbers 1a,1a+d,1a+2d,.....,1a+(n−1)d are in

The correct option is D H.P.The reciprocal of the given numbers is a,a+d,a+2d,.......,a+(n−1)dwhich is an AP with common difference dSo, the given numbers 1a,1a+d,1a+2d,....1a+(n−1)d are in HP.

In general, the numbers $\frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . . . ., \frac{1}{a + (n - 1) d}$ are in

The correct option is D H.P.
The reciprocal of the given numbers is $a, a + d, a + 2 d, . . . . . . ., a + (n - 1) d$
which is an AP with common difference $d$
So, the given numbers $\frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . . . \frac{1}{a + (n - 1) d}$ are in HP.