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# 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

tn = 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

Sn(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

Sn = (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

an = 2a + (n – 1)d … INCORRECT (“2” is extra)
an = a - (n + 1)d … INCORRECT (signs are misplaced)
an = 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 nth term of AP.

Practice Examples

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

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

Using incorrect formulas

Sn = (a + (n – 1)d) … INCORRECT (“2” is missing)
Sn = (2a - (n + 1)d) … INCORRECT (signs are misplaced)
Sn(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 nth term of AP - Taking n instead of n minus 1.

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

Common mistake in finding sum of nth term of AP - missing 2 from 2a.

Practice Examples

1. If the nth term of an A.P. is (2n+1), find the sum of the first n terms of the A.P.
2. If the nth term of an A.P. is (2n+1), find the sum of the first n terms of the A.P.

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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