The sum is:
Sn = (a1+ an)n/2
We need the sun of the first 20 terms, then we will substitute with n= 20
==> s20 = (a1+ a20) * 20/2
==> S20 = 10(a1+ a20)
Given:
a4-a2= 4
a1+ a3+ a5+a6= 30
We know that: if r is the common...
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The sum is:
Sn = (a1+ an)n/2
We need the sun of the first 20 terms, then we will substitute with n= 20
==> s20 = (a1+ a20) * 20/2
==> S20 = 10(a1+ a20)
Given:
a4-a2= 4
a1+ a3+ a5+a6= 30
We know that: if r is the common ratio between numbers:
a2= a1+ r
a4= a1+ 3r
a5= a1+ 4r
a6= a1+ 5r
but: a4- a2= 4
==> a1+ 3r - (a1+r) = 4
==> 2r = 4
==> r= 2
Also:
a1+ a3+ a5+ a6 = 30
==> a1+ a1+2r + a1+ 4r + a1 5r = 30
==> 4a1 + 11r = 30
==> 4a1+ 11*2 = 30
==> 4a1 + 22 = 30
==> 4a1 = 8
==> a1= 8/4= 2
==> a1= 2
Now we will calculate a20:
a20 = a1+ 19*r
= 2 + 19*2= 2 + 38 = 40
==> a20 = 40
==> S20 =10 (a1+ a20)
= 10( 2 + 40)
= 10* 42 = 420
==> S20 = 420