MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Insertion of AP's between 2 Numbers

For an ap if ...

Question

For an ap if tm =1/n and tn=1/m then a-d=

Open in App

Solution

let a be the first term and d be the common difference of an AP series

tm = a+ (m-1)d =1/n ….(i) (given)

tn = a+(n-1)d=1/m …...(ii) (given)

Subtracting equation (ii) from (i)

d[(m-1)-(n-1)] = 1/n -1/m,

d(m-n) = (m-n)/mn,

d = 1/mn ….(iii)

Substituting equation (iii) in (i)

a+(m-1)/mn = 1/n,

a = 1/n[1-(m-1)/m],

a = 1/mn ….(iv)

Hence a-d = 1/mn - 1/mn = 0 Ans.

Suggest Corrections

thumbs-up

13

Similar questions

T_{r}

r

th term of an AP, for

r = 1, 2, . . . .

if for some positive integers

m, n

T_{m} = 1 / n

T_{n} = 1 / m

T_{m / n}

equal to ________

T_{r}

r

th term of an AP whose first term is

a

and common difference is

d

. If for some positive integers

m, n, m \neq n, T_{m} = \frac{1}{n}

T_{n} = \frac{1}{m}

a - d

t_{n}

n^{t h}

S_{n}

n

t_{m} = \frac{1}{n}

t_{n} = \frac{1}{m}

S_{m n}

Q. If in an A.P.,

T_{m} = n, T_{n} = m

d = - 1

T_{r}

be the rth term of an A.P. whose first term is

a

, and common difference is

d

. If for some positive integers

m, n

T_{m} = \frac{1}{n}

T_{n} = \frac{1}{m}

a - d =

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Arithmetic Progression

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Insertion of AP's between 2 Numbers

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon