Find the least value of n for which the sum of the series 20+28+36+..... To n term is greater than 1000
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Answer:
n = 14
Step-by-step explanation:
Find the least value of n for which the sum of the series 20+28+36+..... To n term is greater than 1000
20 + 28 + 36 + ..............n term
a = 20
d = 8
Sn = (n/2)(a + a + (n-1)d)
=> Sn = (n/2)(20 + 20 + (n-1)8)
=> Sn = n(20 + (n-1)4)
=> Sn = n(4n + 16)
=> Sn= 4n² + 16n
Sn > 1000
=> 4n² + 16n > 1000
=> n² + 4n > 250
=> n² + 4n - 250 > 0
n > 13.93
=> n = 14
S₁₄ = (14/2)(20 + 20 + (13*8))
= 7 (144)
= 1008
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