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Priyanshu
answered
1 year(s)
, 5 month(s) ago

The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).

Answer. Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27)

Let’s consider the ratio these two AP’s mth terms as am : a’m →(2)

Recall the nth term of AP formula, an = a + (n – 1)d...

- 5 Answers
- 37 Likes
- 183925 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

If mth term of an A.P is 1/n and the nth term is 1/m

Answer.

- SME Approved

- 2 Answers
- 9 Likes
- 93770 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

In an ap of 50 terms, the sum of 1st 10 terms is 210 and the sum of its last 15 terms is 2565. find the a.p.

Consider a and d as the first term and the common difference of an A.P. respectively.

n th term of an A.P., a_{n} = a + ( n – 1)d

Sum of n terms of an A.P., S n = n/

...- 2 Answers
- 5 Likes
- 75951 Views

Raghunath
answered
4 year(s)
, 1 month(s) ago

If m times the mth term of an AP is equal to n times its nth term, find (m+n)th term.

let the first be
_{} and common difference is
_{}.

Given m times the mth term = n times the nth term

Recall that the nth term of AP is
_{}

...

- 1 Answer
- 4 Likes
- 53764 Views

Agam
answered
1 year(s)
, 5 month(s) ago

The sum of first n terms of an AP is 3n^2+4n find the 25th term of this AP.

Given S
_{n} = 3n
^{2 } + 4n

S
_{1} = 3×1 + 4×1 = 7.

S
_{2} = 3×4 + 4×2 = 12 + 8 = 20.

Therfore First term a
_{1}...

Asked by D narayana

Mar 14

- 4 Answers
- 3 Likes
- 53461 Views

Raghunath
answered
4 year(s)
, 4 month(s) ago

How many three digit numbers are divisible by 7 ?

Sol:

The first three digit number which is divisible by 7 is 105 and last three digit number which is divisible by 7 is 994.

This is an A.P. in which *a* = 105, d = 7 and l = 994.

Let

...- 1 Answer
- 4 Likes
- 46375 Views

Syeda
answered
1 year(s)
, 9 month(s) ago

If pth term of an A.P is 1/q and its qth term is 1/p

Answer.

Given pth term = 1/q

That is a
_{p} = a + (p - 1)d = 1/q

aq + (pq - q)d = 1 --- (1)

Similarly, we get ap + (pq - p)d = 1 --- (2)

From...

- 2 Answers
- 1 Like
- 39401 Views

Agam
answered
1 year(s)
, 5 month(s) ago

If the sum of 3 numbers in a.p. is 12 and the sum of their cubes is 288. find the numbers.

Consider the numbers are a , a+d , a+2d

Given that S3 =12

⇒ a + a + d + a + 2d = 12

3(a + d) =12

a + d = 4

a = 4 - d ------------(1)

And sum of their cubes is

...- 3 Answers
- 3 Likes
- 36473 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

If m times the nth term of an A.P. is equal to n times

Given m × t
_{m} = n × t
_{n}

⇒ m[a + (m – 1)d] = n[a + (n – 1)d]

⇒ ma + m(m – 1)d] = na + n(n – 1)d

⇒ ma + m(m – 1)d] – na – n(n – 1)d = 0

⇒ a(m – n) + [m...

- 4 Answers
- 4 Likes
- 35945 Views

Virat
answered
2 month(s)
, 7 day(s) ago

The angles of a triangle are in AP. If the greatest angle is twice the least, find all the angles.

Let a - d, a, a + d be the three angles of the triangle that form AP.

Given that the greatest angle is twice the least.

Now, 2(a - d) = a + d

2a - 2d = a + d...

- 4 Answers
- 0 Like
- 33663 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Find the middle terms in the ap 20,16,12.............[-176]

Answer.

Given AP is 20,16,12.............[-176]

Here a = 20, d = 16 – 20 = – 4

t_{n} = –176

nth term of an AP is t_{n} = a + (n – 1)d

⇒ –176 = 20 + (n

- 2 Answers
- 0 Like
- 32547 Views

Syeda
answered
1 year(s)
, 9 month(s) ago

A thief runs away from a police station with a uniform speed of 100m/minutes

Answer.

Let the police catch the thief in n minutes

Since the thief ran 1 min before the police start running.

Time taken by the thief before he was caught = (n + 1) min

- 2 Answers
- 2 Likes
- 32485 Views

Syeda
answered
1 year(s)
, 9 month(s) ago

The 4th term is of an AP is zero .Prove that its 25th term is triple its 11th term

Given a
_{4} = 0

That is (a + 3d) = 0

⇒ a = - 3d → (1)

nth term of AP is given by a
_{n} = a + (n – 1)d

a
_{11} = a + 10d = – 3d + 10d = 7d [From (1)]...

Asked by Advitiya rajput

Feb 10

- 3 Answers
- 5 Likes
- 31521 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

ALONG A ROAD LIE AN ODD NUMBER OF STONES PLACED AT INTERVAL OF 10M.

Answer.

Let the number of stones be (2n + 1) since there are odd number of stones.

Given these stones are to be kept around the middle stone.

That is there will n stones ke...

- 2 Answers
- 0 Like
- 30348 Views

Syeda
answered
1 year(s)
, 9 month(s) ago

A man arranges to pay off a debt of Rs 3600 by 40 installments

Answer.

Let the first installments be a

Given that the installments are in AP.

Let the common difference be d

Hence the installments are: a, a + d, a + 2d ………..40^{th}

- 2 Answers
- 0 Like
- 29567 Views

Raghunath
answered
4 year(s)
, 2 month(s) ago

The sum of n, 2n ,3n terms of an AP are S1,S2,S3,respectively. Prove that S3 =3(S2- S1)

Sol:

Let ‘a’ be the first term of the AP and ‘d’ be the common difference

S
_{1} = (n/2)[2a + (n – 1)d] --- (1)

S
_{2} = (2n/2)[2a + (2n – 1)d] = n[2a +...

Asked by Tejaswini p kale

Feb 6

- 1 Answer
- 2 Likes
- 28420 Views

Agam
answered
1 year(s)
, 8 month(s) ago

The sum of n terms of the three arithmetical progressions are S1, S2 and S3

- 2 Answers
- 0 Like
- 27231 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Show that the sum of its first (p+q) terms is -(p+q)?

Answer.

Let a be the first term and d is common difference of the A.P then sum of n terms in A.P

is S
_{n} = (n/2)[ 2a + (n - 1) d]

Given that S
_{p<}...

- 2 Answers
- 2 Likes
- 26012 Views

Syeda
answered
1 year(s)
, 9 month(s) ago

The sum of the 1st n terms of an AP is 5n-n2 Find the nth term of an A.P

Answer.

Given that sum of the first n terms of an AP is 5n - n^{2}

Sn = 5n − n^{2}

First term, a_{1} = S_{1} = 5(1) − (1)^{2} = 5 − 1 = 4

Sum of fir

Asked by Neeraja Babu

Feb 12

- 2 Answers
- 0 Like
- 25317 Views

Kishore
answered
5 year(s)
, 5 month(s) ago

To prove sum of first m+n terms is -(m+n)

- 1 Answer
- 5 Likes
- 25095 Views

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