## Important Concepts and Formulas - Sequence and Series

Comments(33)

priya
16 Nov 2014 7:13 PM

In how many ways can letters of English alphabet be arranged so that there are 7 letters between the letters a and b and no letter is repeated??

Raj
21 Nov 2014 12:37 AM

__Assuming that all arrangements are done by taking all 26 alphabets at a time__

Removing A and B, there are 24 letters. From these letters,

**7**

**alphabets can be arranged between A and B in 24P7 ways**

**A and B can be arranged in 2! ways**

Remaining alphabets = 17

Consider (A)(7 letters)(B) as a single alphabet now

**Lets consider this as a total of 18**

**alphabets . These**

**alphabets can be arranged among themselves in 18! ways**

**Required number of ways = 24P7* 2! * 18!**

reshma
27 Oct 2014 9:21 AM

what is the formula to find the product of gp

PARVEEN
18 Oct 2014 4:09 PM

sum of three numbers in ap is 21 and if one addes to third no and one deducted from 2nd no the series become gp what are the numbers

Raj
23 Oct 2014 10:31 PM

Let numbers be (a-d), a and (a+d)

sum = 3a = 21

a = 7

So the numbers are (7-d), 7 , (7+d)

Given that (7-d), 6, (8+d) are in GP

6

36 = 56 + 7d - 8d -d

d2 + d - 20 = 0

(d+5)(d-4)=0

d = -5 or 4

so numbers are 12, 7, 2

OR

numbers are 3, 7, 11

sum = 3a = 21

a = 7

So the numbers are (7-d), 7 , (7+d)

Given that (7-d), 6, (8+d) are in GP

6

^{2}= (7-d)(8+d)36 = 56 + 7d - 8d -d

^{2}d2 + d - 20 = 0

(d+5)(d-4)=0

d = -5 or 4

so numbers are 12, 7, 2

OR

numbers are 3, 7, 11

vivek
11 Oct 2014 11:42 AM

what is answer for this question

if the 9th term ap is zero then t29/t19=k. where k=?

Raj
16 Oct 2014 10:23 PM

9th term = 0

a + (9-1)d = 0

a + 8d = 0

a = -8d

Anirudh Mishra
16 Oct 2014 10:16 PM

VIVEK, answer for your question is 2

Harshit
04 Sep 2014 1:01 PM

How to you find the sum of a series if the difference of terms of the series are in ap.

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