Class 10 NCERT Maths Solution Exercise-5.3, Arithmetic Progression(A.P).

NCERT MATHS CLASS - X

Arithmetic Progressions

Exercise 5.3

Question 2:

Find the sums given below

(ii) 34 + 32 + 30 + ……….. + 10

(iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

Sol.

Given
a = 7, l = 84


We have to find out value of n.
Let 84 be the n^th term of this A.P.
l = a + (n − 1)d, where l = last term of AP
84 = 7 + (n − 1).7/2
(n − 1).7/2 = 77
(n − 1) = 22
n = 23
The sum of n^th terms of an AP is given by
 


(ii) 34 + 32 + 30 + ……….. + 10

Given
a = 34, d = a₂ − a₁ = 32 − 34 = −2
l = 10
Let 10 be the n^th term of this A.P.
Last term is given by
l = a + (n − 1) d
10 = 34 + (n − 1) (−2)
−24 = (n − 1) (−2)
12 = n − 1
n = 13
 



(iii) (−5) + (−8) + (−11) + ………… + (−230)
Given
a = −5, l = −230
d = a₂ − a₁ = (−8) − (−5)
   =− 8 + 5 = −3
Let −230 be the n^th term of this A.P.
l = a + (n − 1)d

−230 = − 5 + (n − 1) (−3)

−225 = (n − 1) (−3)

(n − 1) = 75

n = 76

And,

 

 




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