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Priyanshu answered 1 year(s) , 3 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...

Asked by Venkatesh

Nov 13

  • 5 Answers
  • 32 Likes
  • 149906 Views
Syeda answered 1 year(s) , 8 month(s) ago

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

Answer.


  • SME Approved

Asked by Lavanya

Nov 24

  • 2 Answers
  • 7 Likes
  • 69465 Views
Agam answered 1 year(s) , 3 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  + 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
  • 48269 Views
Syeda answered 1 year(s) , 8 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., an = a + ( n – 1)d

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

...

Asked by Ishita

Feb 27

  • 2 Answers
  • 4 Likes
  • 44357 Views
Raghunath answered 4 year(s) , 2 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

...

Asked by Manish

Nov 21

  • 1 Answer
  • 4 Likes
  • 39081 Views
Raghunath answered 3 year(s) , 11 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
...

Asked by David

Feb 19

  • 1 Answer
  • 2 Likes
  • 34636 Views
Syeda answered 1 year(s) , 7 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...

Asked by Saumya

Mar 11

  • 2 Answers
  • 1 Like
  • 34516 Views
Syeda answered 1 year(s) , 8 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...

Asked by Ajay

Oct 23

  • 4 Answers
  • 4 Likes
  • 34495 Views
Syeda answered 1 year(s) , 8 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
tn = –176
nth term of an AP is tn = a + (n – 1)d
⇒ –176 = 20 + (n

...

Asked by Narasimha

Oct 26

  • 2 Answers
  • 0 Like
  • 29724 Views
Agam answered 1 year(s) , 3 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

...

Asked by Ishita

Feb 11

  • 3 Answers
  • 3 Likes
  • 29522 Views
Virat answered 6 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...

Asked by David

Feb 19

  • 4 Answers
  • 0 Like
  • 28001 Views
Syeda answered 1 year(s) , 7 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

...

Asked by Gamsy

Feb 19

  • 2 Answers
  • 2 Likes
  • 26951 Views
Syeda answered 1 year(s) , 7 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)]...

  • 3 Answers
  • 5 Likes
  • 25747 Views
Syeda answered 1 year(s) , 8 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...

Asked by Venkatesh

Nov 13

  • 2 Answers
  • 0 Like
  • 25566 Views
Syeda answered 1 year(s) , 7 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 ………..40th

...

Asked by Gajaanan

Oct 28

  • 2 Answers
  • 0 Like
  • 24888 Views
Syeda answered 1 year(s) , 8 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<...

Asked by Navin

Sep 18

  • 2 Answers
  • 2 Likes
  • 24046 Views
Syeda answered 1 year(s) , 7 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 - n2
Sn = 5n − n2
First term, a1 = S1 = 5(1) − (1)2 = 5 − 1 = 4
Sum of fir

...

Asked by Neeraja Babu

Feb 12

  • 2 Answers
  • 0 Like
  • 22944 Views
Priyanshu answered 1 year(s) , 3 month(s) ago

find sum of first 15 terms of an ap. whose nth term is 3-2n

Given nth term of AP a n = 3 - 2n
Put n = 1, we get
a 1 = 3 - 2 = 1
Put n = 2, we get a 2 = 3 - 4 = - 1
Hence d = -1 - 1 = -2
a15 = 3- 30 = - 27
Sum of 15 term...

Asked by Sweta

Dec 28

  • 3 Answers
  • 0 Like
  • 22588 Views
Raghunath answered 3 year(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 +...

  • 1 Answer
  • 2 Likes
  • 22053 Views
Syeda answered 1 year(s) , 7 month(s) ago

FIND THE NUMBER OF NATURAL NUMBERS BETWEEN 101 AND 999 WHICH ARE BOTH DIVISIBLE BY BOTH 2 AND 5?

Answer.

a = 110 {first number to be divided by 2 and 5}
difference d =10
a n=990  {last no to be divided by 2 and 5}
an = a + {n - 1}d
990 = 110 + 10n -10 <...

Asked by Sreejesh

Mar 14

  • 2 Answers
  • 3 Likes
  • 22016 Views
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