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The sum of the four terms in arithmetic progression is 18 and the sum of their squares is 326. find the number?

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by adrian22

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by adrian22

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An arithmetic progression is a sequence in which they have a common difference. A sequence is shown as:

in which d is the common difference

So we know that:

Let us make

Remember that this is an arithmetic progression so the terms are respectively

or

Since d is their common difference

We plug in the values to the second equation in the given

The squareroot of 49 is either positive or negative 7.

So remember that

If d=7

When n=1

m=1-7=-6

n=1

o=1+7=8

p=8+7=15

If d=-7

When n=8

m=8-(-7)=15

n=8

o=8-7=1

p=1-7=-6

Therefore the numbers are -6, 1, 8 and 15

in which d is the common difference

So we know that:

Let us make

Remember that this is an arithmetic progression so the terms are respectively

or

Since d is their common difference

We plug in the values to the second equation in the given

The squareroot of 49 is either positive or negative 7.

So remember that

If d=7

When n=1

m=1-7=-6

n=1

o=1+7=8

p=8+7=15

If d=-7

When n=8

m=8-(-7)=15

n=8

o=8-7=1

p=1-7=-6

Therefore the numbers are -6, 1, 8 and 15