In this worksheet, we will practice determining whether a geometric series is convergent and finding its limit.
Q1:
Can the sum of an infinite geometric series with common ratio 𝑟 be found when |𝑟|<1?
Q2:
Find the sum of the infinite geometric sequence 49,−21,9,….
Q3:
Can the sum of an infinite geometric series be found for any value of 𝑟 satisfying |𝑟|≤1?
Q4:
Find the possible infinite geometric series where the sum is −21 and the sum of the first and second terms is −353.
Q5:
Find the sum of an infinite number of terms of the geometric sequence 87,√87,1,….
Q6:
Find the common ratio of an infinite geometric sequence given the sum is 52 and the first term is 14.
Q7:
Find the infinite geometric sequence given each term of the sequence is twice the sum of the terms that follow it and the first term is 37.
Q8:
Find the sum of an infinite number of terms of a geometric sequence given the first term is 265 and the fourth term is −650343.
Q9:
Find the sum of the infinite geometric sequence 7,(−7),7,….
Q10:
Find the sum of the squares of the terms of an infinite geometric sequence given the first term is 49 and the common ratio is 9𝑥.
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