Re: Consider a sequence of numbers given by the expression 5 + (
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27 Jan 2013, 20:26
Responding to a pm:
HI Karishma
I need to clarify a logical doubt on the question.
If the value of n is put in the formula and sequence of number is obtained, we get the following
5,8,11,14,17,...................................,245,248,251,254,257
Formula that i know to find out the number of terms in a sequence (A.P.) or more precisely number of multiples of x in a sequence (A.P.) is
[(Last multiple of x in the range - first multiple of x in the range)/x] + 1
hence
Last multiple of 7 in the sequence is 245
First multiple of 7 in the sequence is 14
Hence total multiple of 7 in the sequence is [(245- 14)/7]+1 = 34
Its not even mentioned in the answer choices ...i know there is a basic fundamental error in my approach......
Analogy to above question which i used was:-
Question:- Find the total number of multiples of 4 from 20 to 99?
I use the same formula as above
[(96-20)/4]+1
=20 and it is the correct answer.....
Is there any difference between the two questions...both are A.P sequence....
Pls help me in getting my fundamental correct....
Important: It is good to know formulas since they help us save time but you must know the exact inputs and limitations of every formula you would like to use.
The formula you used is absolutely fine and very useful actually. This is what happens in the 2nd question:
Question:- Find the total number of multiples of 4 from 20 to 99.
The given sequence is 20, 21, 22, 23, 24, 25, 26, 27, 28, ... 96, 97, 98, 99
You need to find the multiples of 4 in this sequence which are 20, 24, 28, ... 96 (this is an AP)
20 is the first multiple and 96 is the last. The common difference between two consecutive multiples is 4. So you use the AP formula as you have done. Great.
The original question is a little different.
\(5 + (n - 1) * 3=3n+2\)
Putting values for n, the sequence we get is this: 5,8,11,14,17, 20, 23, 26, 29, 32, 35, 38, ...................................,245,248,251,254,257
We need to find the multiples of 7 in this sequence which are 14, 35, ... 245 (mind you, we need the multiples of 7 which appear in this sequence - 21, 28 do not appear in this sequence)
The first multiple is 14 and the last is 245 and the common difference is 21.
Now use the formula: (245 - 14)/21 + 1 = 12 and that's your answer!