Given that,
a2+(ar)2+(ar2)2=33033,(a,r∈N)
⇒a2(1+r2+r4)=112×273
On comparing both sides of the equation we get,
a=11 and 1+r2+r4=273
⇒r2+r4=272
⇒r2(1+r2)=16×17
⇒r=4
Now a+ar+ar2=11+11×4+11×16
=11+44+176=231.
Therefore, the required value is 231
Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to
Held on 10 Apr 2023 · Verified 6 Jul 2026.
241
231
210
220
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