Page 39 - Mathematics Class - X

INFERENCE
n
The sum of first n terms of an AP, S = n [2a + (n − 1) ] d
2

EXTENDED TASK
Find the sum of first n terms of the list of numbers 1 , 2 , 3 , ...
2
2
2
APPLICATION
This result may be used to find the sum of first n terms of the list of numbers like 1 , 2 , 3 , ... which is to be studied
3
3
3
in Class XI.

Viva-Voce

1. What is the formula for general term of an A.P.?
Ans. T = a + (n – 1) d
n
where, a → First term

d → common difference
n → nth term

2. Write the formula for nth term of an A.P. from the end.
Ans. nth term from the end = l – (n – 1)d,

Where l is last term and d is the common difference.

3. What number should be inserted between a and b such that the three numbers are in A.P.?
a + b
Ans. The required number is .
2

4. What is the formula for the sum of n terms of an A.P.?
n
Ans. S = {2a + (n − 1) }, where a, b and n are the first term, common difference and total no. of terms of an
d
n
2
A.P. respectively.
5. Find the sum of the first n natural numbers.
Ans. First n natural numbers are 1, 2, 3, 4 ... (n – 1), n.

It is an A.P., where a = 1 and d = 1.
Now, the sum of first n natural numbers is given by

n nn 1) n
( +
S = (2 +− 1) = [using S = [2a + (n − 1) ] d
n
n 2 2 n 2

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