Question

The arithmetic mean of seven numbers which are in arithmetic progression is 100.Find the largest number in progression if the smallest is 10

Answer 1

Sum of arithmetic mean is 7 × 100 = 700. The smallest number is 'a' which is here 10 and largest number is 'a + 6d' which will be 190.

Answer 2

Concept

Arithmetic Progression (AP) in mathematics is a sequence of numbers, in which the difference between any two consecutive numbers is a constant value.

Given

1) AM of 7 numbers is 100

2) These 7 numbers are in AP

3) Smallest number is 10

Find

The value of largest number

Solution

If a and b are the numbers then

AM = (a+b)/2

Let the seven numbers in AP be

a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d

AM of these 7 numbers

AM  = (a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d)/7

AM = 100

(a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d)/7 = 100

a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d = 700

7a + 21d= 100

We are given that smallest number is 10

a = 10

7(10) +21d = 700

70 + 21d = 700

21d = 630

d = 30

a+6d = 10 + 6(30)

a+6d = 10 + 180

a+6d = 190

The value of largest number is 190

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