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Sagot :
Answer:
- (a) 10, (b) 21, (c) 8, (d) 255, (e) 25
Step-by-step explanation:
(a)Total number of candies = 120
The number of candies in the rows form AP sequence:
- 3, 5, 7, ...
The first term is a=3 and common difference is d=2
Sum of n terms:
- S = 1/2n(2a + (n - 1)d)
Substitute values and solve for n:
- 120 = 1/2n(2*3 + 2(n - 1))
- 120 = 3n + n² - n
- n² + 2n = 120
- n²+ 2n + 1 = 121
- (n + 1)² = 121
- n + 1 = 11
- n = 10
Correct choice is (ii) 10
(b) Formula for nth term:
- a(n) = a + (n - 1)d
- a(10) = 3 + 9*2 = 3 + 18 = 21 candies
Correct choice is (ii) 21
(c) Use same formula:
- a(7) - a(3) = a + 6d - a - 2d = 4d
- 4d = 4*2 = 8
Correct choice is (i) 8
(d) Sum of candies in 15 rows
- S(15) = 1/2(15)(2*3 + (15 - 1)*2) = 1/2(15)(6 + 28) = 255
Correct choice is (iii) 255
(e) Number of candies in 12th row:
- a(12) = 3 + (12 - 1)*2 = 3 + 22 = 25
Correct choice is (iii) 25
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