SOLUTION: Find the number of terms in the arithmetic progression 1, 3 , 5,....101

Algebra.Com
Question 1162164: Find the number of terms in the arithmetic progression 1, 3 , 5,....101

Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
General term, ;
Last term being 101, ;

Answer by ikleyn(52840)   (Show Source): You can put this solution on YOUR website!
.

Consider all natural numbers from 1 to 101, inclusive.


Their amount is 101.


From this amount, exclude all even natural numbers from 1 to 100 ---  their amount is   = 50.


The difference  101 - 50 = 51  is your answer.

Solved.

-------------------

This problem is accessible for the 3-rd - 4-th young students,
who do not know yet neither arithmetic sequences nor equations.

Nevertheless, this problem is a good exercise for the young minds.

So, the solution to the problem must be accessible for them, too.

In other words, the solution should be adequate to the problem.

It is why I came with my post.



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Another path to the answer without algebra, accessible to young students....

The first term is 1; each term is 2 more than the preceding term; the last term is 101.

How many 2's do you need to add to the first term, 1, to get the last term, 101? Answer: (101-1)/2 = 100/2 = 50.

So there are 50 terms after the first one; that means there are 51 terms.


RELATED QUESTIONS

Find the number of terms in an Arithmetic Progression whose first term is 5 common... (answered by ikleyn)
Given the arithmetic progression -1/6,1/12,1/3...find the 10th term and the sum of the 12 (answered by psbhowmick)
The first and the last term of an arithmetic progression are 9 and 93.If the sum of the... (answered by mananth,stanbon)
One sequence of alternating terms of the series 1+2+3+4+5+8+... forms an arithmetic... (answered by ikleyn)
A geometric progression has 6 terms. The first term is 192 and the common ratio is 1.5.... (answered by greenestamps)
A geometric progression has six terms. The first term is 486 and the common ratio is ;.... (answered by greenestamps)
A geometric progression and an arithmetic progression have the same first term. The... (answered by htmentor)
The first term of an arithmetic progression is 8 and the last term is 34. The sum of the (answered by MathLover1)
find the first five terms of the arithmetic progression whose seventh and twenty-third... (answered by ikleyn,josgarithmetic)