Question

Find the least value of n for which the sum of the series 20+28+36+..... To n term is greater than 1000

Answer 1

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