Arithmetic progression. I have to find out the first term and the ratio! We know the third term = 8 and the seventh term of progression= 20.

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We know the formula for any term of an arithmetic progression:

an=a1 + (n-1)r, where a1 is the first term and r is the ratio.

a3=a1 + (3-1)r

a7=a1 + (7-1)r

Doing the substitution where we know the values

8 = a1 + 2r

20 = a1 + 6r

We are subtracting the second relation from the first one and the result will be

8-20 = a1 + 2r -a1 - 6r

-12 = -4r


With the known value of r, we go back in the first relation and making substitution of r

8 = a1 + 2r

8 = a1 + 2x3

8 = a1 + 6

a1= 8-6


revolution's profile pic

revolution | College Teacher | (Level 1) Valedictorian

Posted on

Formula of arithmetic progression of the nth term would be:


where a1: the initial term of an arithmetic progression

s: common difference of successive numbers

You know the third term is 8 so:

8= a1+(3-1)s


You know that the seventh term is 20 so:

20= a1+(7-1)s - eqn 1

20=a1+6s - eqn 2

Subtract eqn 1 from eqn 2





So, use this value and substitute into eqn 2

20= a1+6(3)




The first term would be 2