Question

a man eat 100 grapes in 5 days.each day he eat 6 more grapes than those he ate on previous day. how many grapes did he eat the first day?​

Answer 1

Method 1)

Given:-

• Sn = 100
• n = 5
• d = 6

Find:-

Number of grapes he eat the first day.

Solution:-

Sn = n/2 [2a + (n - 1)d]

Substitute the known values in above formula

= 100 = 5/2 [2a + (5 - 1)6]

= 100(2) = 5(2a + 24)

= 200/5 = 2a + 24

= 40 = 2a + 24

= 2a = 40 - 24

= 2a = 16

= a = 8

•°• $\sf{\underline{Man\:eat\:8\:grapes\:first\:day}}$

Method 2)

Let number of grapes he eat first day be x.

A man eat 100 grapes in 5 days, each day he eat 6 more grapes than those he ate on previous day.

According to question,

= x + (x + 6) + (x + 12) + (x + 18) + (x + 24) = 100

= 5x + 60 = 100

= 5x = 40

= x = 8

•°• $\sf{\underline{Man\:eat\:8\:grapes\:first\:day}}$

Answer 2

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Answer:

8 grapes he eat the first day.

Step-by-step explanation:

We can solve this question in a very easiest way.

Let assume that the number of grapes eat first day be y.

According to the question,

=> x + (x + 6) + (x + 12) + (x + 18) + (x + 24) = 100

=> 5x + 60 = 100

=> 5x = 100 - 60

=> 5x = 40

=> x = 40/5

.°. x = 8

Therefore, 8 grapes he eat the first day.

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The another method is also used for solving this question. By using the formula of the sum of an arithmetic progression.

Given,

Sum of an A.P. = 100

n = 5

d = 6

By using the formula of the sum of an arithmetic progression.

Sn = n/2 [2a + (n-1) d]

Substitute the given values.

=> 100 = 5/2[2a + (5-1) 6]

=> 100 × 2 = 5[2a + (5-1) 6]

=> 200 = 5[2a + (5-1) 6]

=> 200/5 = 2a + 24

=> 40 = 2a + 24

=> 2a = 40 - 24

=> 2a = 16

.°. a = 8

Therefore, 8 grapes he eat the first day.

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