Why is it 15th term but not 14th term?
In this sum
Q.find the 11th term from the last term of the ap 10 7 4 - 62 .
Sol: an=a + (n-1)d
-62=10+(n-1)(-3)
-62=10-3n+3
3n=75
n=25
term 15 from the first term = term 11 from last term
1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15, 16,17,18,19,20,21,22,23,24,25
a15=a+14x-3
a15=10-42 = - 32
Answers
See the question given below as an example.
20 books are arranged in a book shelf. 6th book ordered from left is taken from them. What should be the position of this book ordered from right?
Here, the method to find the answer is, add 1 to 20 and then subtract 6. We get 15.
Okay, let the books are numbered in the following (ordered from left):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
When it is ordered from right, we get the following:
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Here, 6 is at the 15th place. Why it's not at 14th place?!
Okay, let me say a basic thing according to this.
When we subtract 6 from 20, we get 14, which indicates the no. of 7th book to 20th book. Not 6th book to 20th book.
Which means, 6 subtracted from 20 gives 14 books which are,
7 8 9 10 11 12 13 14 15 16 17 18 19 20
As an example, 5 is away from 2 by 3 numbers 3, 4, 5. So that 5 - 2 = 3. It doesn't include 2. To include, you must add 1 to 5 before subtraction!
As an example again, in a calendar, no. of days upto March 10 after March 2 is counted by all people as the following:
March 3, March 4, March 5, March 6, March 7, March 8, March 9, March 10.
Does it contain March 2?! Never!
To contain it, 1 must be added to March 10 before subtraction.
According to these examples, 1 must be added to 20 before subtracting 6, so to get 15, as the position of 6th book ordered from right is equal to the no. of books after 5th book, not 6th book. Because it should include 6th book.
As another example, take your right hand and find the position number of your middle number counted from both pinky finger and thumb each. Why 3 comes in both cases?!
The answer here is 5 + 1 - 3 = 3.
Okay, now let's come to your Q&A.
25 terms are given there.
11th term from last term is asked about.
The position of 11th term from 25th term can be counted ordered from right as below:
25 24 23 22 21 20 19 18 17 16 15
Let these be a set.
As the answer is 25 + 1 - 11 = 15 (here)
Okay.
For the position of 11th term from last, ordered from left, we have to subtract first 14 terms, and we get the set given above. It starts with 15 (ordered from left), so the answer is 15 (here).
Hope this helps you. ^_^
Please ask me if you've any any doubt!!! I'm also confused on it.
The answer is on my own words only and I didn't copy from any source. Why should I want to do it?!
Please mark it as the brainliest if this helps you.
Thank you. :-))
Concept:
When its a range , like x to y and you need to count theno. of terms, us ethis formula
y-x+1
Given:
Q.find the 11th term from the last term of the ap 10 7 4 - 62 .
Sol: an=a + (n-1)d
-62=10+(n-1)(-3)
-62=10-3n+3
3n=75
n=25
term 15 from the first term = term 11 from last term
1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15, 16,17,18,19,20,21,22,23,24,25
a15=a+14x-3
a15=10-42 = - 32
Find:
Whether it is 15th term or 14th term
SOLUTION:
Whenever you need to count between the ranges like 30-60, you can normally say its 30, but it's not, its 60-30+1=31, because you you forgot to count 30 in your counting.
So, here there is 25 books, count 11 from behind with same formlua i explained above,
Let the unknown term be x,
25-x+1=11
⇒26-11=x
⇒x=15
So here we got 15
Therefore ,it is 15th term not 14
#SPJ2