If the first and the last terms of an arithmetic series are 10 and 62, show that the sum of the series varies directly as the number of terms.

This shows that the sum of the series varies directly as the number of terms.

Step-by-step explanation:

The terms of the airthmetic series is given by .

Where is the first term .

n represented the number of terms in the airthmetic series .

d is the common difference .

As given

If the first and the last terms of an arithmetic series are 10 and 62 .

Putting in the above

62 - 10 = (n-1)d

52 = (n-1)d

The Sum of the nth terms of the airthmetic series is given by .

Putting the values in the above

(This is for the n terms )

Therefore this shows that the sum of the series varies directly as the number of terms.

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step-by-step explanation: lol

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x