Find the sums given below :
(i) 7 + 10 ½ + 14 +... + 84
(ii) 34 + 32 + 30 +... + 10
(iii) - 5 + (- 8) + (- 11) +... + (- 230)

Name: Find the sums given below : (i) 7 + 10 ½ + 14 +... + 84 (ii) 34 + 32 + 30 +... + 10 (iii) - 5 + (- 8) + (- 11) +... + (- 230)
Uploaded: 2020-04-23T14:11:37Z
Duration: 8 min 44 s
Description: The sum of the following A.P. terms is as follows, for the first A.P. , 7 + 10 ½ + 14 +... + 84, the sum is 1046.5, for the second A.P., 34 + 32 + 30 +... + 10, the sum is 286, for the third A.P., - 5 + (- 8) + (- 11) +... + (- 230), the sum is - 8930.

Solution:

The sum of the first n terms of an Arithmetic Progression is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l], and the nth term of an AP is aₙ = a + (n - 1)d

Here, a is the first term, d is the common difference and n is the number of terms and l is the last term.

(i) 7 + 10 ½ + 14 + .... + 84

Given,

First-term, a = 7
Common Difference, d = 10 ½ - 7 = 21/2 - 7 = 7/2
Last term, l = 84

To find the total number of terms, we will use the formula a + (n - 1) d.

l = aₙ = a + (n - 1) d

84 = 7 + (n - 1) 7/2

77 = (n - 1) 7/2

22 = n - 1

n = 23

Hence, n = 23

Sₙ = n/2 [a + l]

S₂₃ = 23/2 [7 + 84]

= (23/2) × 91

= 2093/2

= 1046 ½

(ii) 34 + 32 + 30 + .... + 10

Given,

First term, a = 34
Common Difference = 32 - 34 = -2
Last term, l = 10

To find the total number of terms, we will use the formula aₙ = a + (n - 1) d.

l = a + (n - 1) d

10 = 34 + (n - 1) (- 2)

n - 1 = 12

n = 13

Hence, n = 13

Sₙ = n / 2 [a + l]

S₁₃ = 13/2 [34 + 10]

= (13/2) × 44

= 13 × 22

= 286

(iii) - 5 + (- 8) + (- 11) + .... + (- 230)

Given,

First-term, a = -5
Common Difference, d = (- 8) - (- 5) = - 8 + 5 = - 3
Last term, l = - 230

To find the total number of terms, we will use the formula a + (n - 1) d.

l = a + (n - 1)d

- 230 = (- 5) + (n - 1)(- 3)

n - 1 = 225/3

n = 75 + 1

n = 76

Hence, n = 76

Sₙ = n/2 [a + l]

= 76/2 [(- 5) + (- 230)]

= 38 [- 235]

= - 8930

☛ Check: NCERT Solutions for Class 10 Maths Chapter 5

Video Solution:

Find the sums given below : (i) 7 + 10 ½ + 14 +... + 84 (ii) 34 + 32 + 30 +... + 10 (iii) - 5 + (- 8) + (- 11) +... + (- 230)

Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.3 Question 2

Summary:

The sum of the following A.P. terms is as follows, for the first A.P. , 7 + 10 ½ + 14 +... + 84, the sum is 1046.5, for the second A.P., 34 + 32 + 30 +... + 10, the sum is 286, for the third A.P., - 5 + (- 8) + (- 11) +... + (- 230), the sum is - 8930.

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