Mathematics: Find the smallest number of terms which may be taken in order that the sum of the arithmetical series 325+350+375+may exceed 10000

The answer to your crossword is prism...

Find the smallest number of terms which may be

Ответ:

InfinityVicky

21.01.2022

Step-by-step explanation:

$a_n=a_1+d(n-1)\\a_n=325+25(n-1)\\.\quad =325+25n-25\\.\quad =25n+300\\\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\10000 =\dfrac{325+(25n+300)}{2}\cdot n\\\\\\10000=\dfrac{(25n+625)n}{2}\\\\\\20000=25n^2+625n\\\\\\0=25n^2+625n-20000\\\\\\0 = n^2+25n-800\qquad \text{(divided by 25)} \\\\\\n=18.4\qquad n=-43.4\qquad \text{(use quadratic formula to solve)}$

Since we can't have a negative number of terms,

n = -43.4 is an extraneous solution

--> n = 18.4 is the only valid solution

In order to EXCEED 10000, n must be GREATER THAN 18.4

The first integer greater than 18.4 is ....

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Find the smallest number of terms which may be taken in order that the sum of the arithmetical series 325+350+375+may exceed 10000

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