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Priyanshu answered 1 year(s) , 7 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...

Nov 13

• 38 Likes
• 187524 Views

Nov 13

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

• SME Approved

Nov 24

• 9 Likes
• 96458 Views

Nov 24

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/

...

Feb 27

• 5 Likes
• 79408 Views

Feb 27

Raghunath answered 4 year(s) , 3 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
...

Feb 19

• 4 Likes
• 56549 Views

Feb 19

Agam answered 1 year(s) , 7 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...

Mar 14

• 3 Likes
• 54581 Views

Mar 14

Raghunath answered 4 year(s) , 6 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

...

Nov 21

• 4 Likes
• 50913 Views

Nov 21

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

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...

Mar 11

• 1 Like
• 40400 Views

Mar 11

Agam answered 1 year(s) , 7 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

...

Feb 11

• 3 Likes
• 38272 Views

Feb 11

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...

Oct 23

• 4 Likes
• 36435 Views

Oct 23

Virat answered 4 month(s) , 10 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...

Feb 19

• 0 Like
• 35246 Views

Feb 19

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

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

...

Oct 26

• 0 Like
• 33319 Views

Oct 26

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

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

...

Feb 19

• 2 Likes
• 33083 Views

Feb 19

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

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

...

Oct 28

• 0 Like
• 33063 Views

Oct 28

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)]...

Feb 10

• 5 Likes
• 32446 Views

Feb 10

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

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...

Nov 13

• 0 Like
• 31044 Views

Nov 13

Raghunath answered 4 year(s) , 4 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 +...

Feb 6

• 2 Likes
• 29451 Views

Feb 6

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

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

Nov 24

• 0 Like
• 27882 Views

Nov 24

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

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<...

Sep 18

• 2 Likes
• 27095 Views

Sep 18

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

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

...

Feb 12

• 0 Like
• 25864 Views

Feb 12

Priyanshu answered 1 year(s) , 7 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...

Dec 28

• 0 Like
• 25765 Views

Dec 28

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