Common Mistakes Made in ICSE Class 10 Board Exams - Chapter Arithmetic Progression

Chapter overview

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term, except the first term.

Consider the following example:

5, 8, 11, 14, 17, 20,…..

Each number is called a term in the Arithmetic progression.

Here 5 is the first term, which can be denoted by ‘a’.

The common difference, denoted by ‘d’, is given by 

8 – 5 = 3

or

11 – 8 = 3

or

14 – 11 = 3

or

17 – 14 = 3

or

20 – 17 = 3

Now, if the first term of an A.P. is ‘a’ and the common difference is ‘d’, then the general term of an A.P. is given by 

t_n = a + (n – 1)d

If the first term of an A.P. is ‘a’ and the common difference is ‘d’, then the sum of the first ‘n’ terms of an A.P. is given by

S_n = (2a + (n – 1)d)

If the last term of an A.P. is ‘l’ is known, then the sum of ‘n’ terms of an A.P. is given by

S_n = (a + 1)

Three or More Terms in A.P.

Sometimes we require certain number of terms in A.P. The following ways of selecting terms are generally very convenient.



Remember:

• When same non-zero number is added or subtracted from each term of an A.P., the resulting sequence is also an A.P.
• When each term of an A.P. is multiplied or divided by a given non-zero fixed number, the resulting sequence is also an A.P.

Topics found difficult or confusing by candidates

Finding the nth term of an A.P. 

Using incorrect formulas

a_n = 2a + (n – 1)d … INCORRECT (“2” is extra)
a_n = a - (n + 1)d … INCORRECT (signs are misplaced)
a_n = a + (n – 1)d … CORRECT FORMULA

Calculation errors

1. Forgetting to multiply d with n – 1
2. Taking the wrong value of (n-1)
3. Subtraction error while finding the common difference

Videos:

Common mistake in finding n^th term of AP.

 

Practice Examples

1. Find the 31^st term of an AP whose 11^th term is 38 and 16^th term is 73.
   Solution: Click here
2. Which term of the AP 3,8,13,18.....is. 78?
   Solution: Click here

Finding the sum of the first n terms of the A.P.

Using incorrect formulas

S_n = (a + (n – 1)d) … INCORRECT (“2” is missing)
S_n = (2a - (n + 1)d) … INCORRECT (signs are misplaced)
S_n = (2a + (n – 1)d) … CORRECT FORMULA

Calculation errors

1. Multiplication error – multiplication of (n - 1)d
2. Division error – forgetting to divide n by 2

Videos:

Common mistake in finding sum of n^th term of AP - Taking n instead of n minus 1.



Common mistake in finding sum of n^th term of AP - missing n by 2.



Common mistake in finding sum of n^th term of AP - missing 2 from 2a.

Practice Examples

1. If the n^th term of an A.P. is (2n+1), find the sum of the first n terms of the A.P.
   Solution: Click here
2. If the n^th term of an A.P. is (2n+1), find the sum of the first n terms of the A.P.
   Solution: Click here

Conclusion

To overcome the challenges faced by the students in the chapter on Arithmetic Progression, one should practice writing the formulas many times to remember them and try solving more examples to have a firm grip on calculations. 

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