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10th CBSE math solution for exercise 5.3 part 3

(ii) Given a = 7, a₁₃
= 35 find d and S₁₃

Solution:

a n = a + (n - 1) d

a₁₃ = 7 + (13 - 1) d

35 - 7 = 12 d

28/12 = d

d = 7/3

S n = (n/2) [a + l]

S₁₃= (13/2) [7 + 35]

= (13/2) (42)

= 13 (21)

= 273

(iii) Given a₁₂
= 37 , d = 3 find a and S₁₂

Solution:

a n = a + (n - 1) d

a₁₂ = a + (12 - 1) 3

37 = a + 11 (3)

37 = a + 33

37 - 33 = a

a = 4

S n = (n/2) [a + l]

S₁₂= (12/2) [4 + 37]

= 6 (41)

= 246

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