NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 11

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 11

Question:

If the sum of the first n terms of an AP is 4n – n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Given:

The sum of the first n terms of an AP is given by Sn = 4n – n2

To Find:

First term (S1), 

sum of first two terms (S2), 

second term (a2), 

third term (a3), 

tenth term (a10), and 

nth term (an).

Formula:

Sn = n2(2a + (n-1)d) , 

an = a + (n-1)d

Solution:

a1 = 4(1) – (1)2 = 3 ⇒ First term = 3

S2 = 4(2) – (2)2 = 4 ⇒ Sum of first two terms = 4

a2 = S2 – S1 = 4 – 3 = 1 ⇒ Second term = 1

Common difference (d) = a2 – a1 = 1 – 3 = -2

a3 = a1 + 2d = 3 + 2(-2) = -1 ⇒ Third term = -1

a10 = a1 + 9d = 3 + 9(-2) = -15 ⇒ Tenth term = -15

an = a1 + (n-1)d = 3 + (n-1)(-2) = 5 – 2n ⇒ nth term = 5 – 2n

Result:

First term = 3, 

Sum of first two terms = 4, 

Second term = 1, 

Third term = -1, 

Tenth term = -15, 

nth term = 5 – 2n

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