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In this lesson, we will learn how to find the summation of a finite geometric series or the nth partial sum of an infinite geometric series to a particular term.

Q1:

Find the sum of the geometric series 1 7 6 + 8 8 + 4 4 + ⋯ + 1 1 .

Q2:

Find the sum of the geometric series 1 7 9 2 + 8 9 6 + 4 4 8 + ⋯ + 2 8 .

Q3:

Find the sum of the first 6 terms of the geometric series 1 2 + 1 4 + 1 8 + 1 1 6 + ⋯ .

Q4:

Find the sum of the first 6 terms of the geometric series 3 5 + 3 1 0 + 3 2 0 + 3 4 0 + ⋯ .

Q5:

Find the sum of the first 20 terms of the geometric sequence 1 , 1 . 0 7 , 1 . 0 7 , 1 . 0 7 , … 2 3 giving the answer to two decimal places.

Q6:

Find the sum of the first 8 terms of the geometric sequence 1 , 1 . 1 8 , 1 . 1 8 , 1 . 1 8 , … 2 3 giving the answer to two decimal places.

Q7:

Find the sum of the first 6 terms of the geometric sequence ( 4 0 5 , 1 3 5 , 4 5 , … ) .

Q8:

Find the sum of the first 6 terms of the geometric sequence ( 8 , − 1 6 , 3 2 , … ) .

Q9:

The table below represents the salary of an employee in three consecutive years. The salary can be described by a geometric sequence. Find the total salary of the employee over five years.

Q10:

Find the geometric sequence and the sum of the first six terms given the second term is four times the fourth one, the sum of the fourth and seventh terms is 2 and all terms are positive.

Q11:

Find the sum of the geometric series 3 2 2 − 1 2 2 + 1 6 6 − ⋯ − 1 1 7 8 2 .

Q12:

Find the sum of the geometric series 1 − 1 2 + 1 4 − ⋯ + 1 2 5 6 .

Q13:

Find the geometric sequence and the sum of the first six terms given that the sum of the second and fourth terms is − 6 8 and the sum of the third and fifth terms is − 2 7 2 .

Q14:

Find the sum of the first 7 terms of a geometric sequence given 𝑇 = − 8 𝑇 5 2 and 𝑇 + 𝑇 = − 6 4 4 6 .

Q15:

Find the number of terms of the geometric sequence 𝑇 = 9 6 × 2 𝑛 𝑛 − 6 for which the sum is equal to 93.

Q16:

Find the least number of terms of the geometric sequence given the first term is 1 and the fourth term is 125, where the sum of the terms is 7 143.

Q17:

In a geometric sequence, the first term is 𝑎 , the common ratio is 𝑟 , and the last term is 𝑙 .

Find the sum of the geometric sequence with 𝑎 = 1 4 0 8 , 𝑟 = 1 2 , and 𝑙 = 8 8 .

Q18:

Find the first term of the infinite geometric sequence where the common ratio is 1 4 and the sum is 9 8 6 7 .

Q19:

Find the geometric sequence and the sum of the first five terms given the sum of the first three terms is 1 and the sum of the next three terms is 27.

Q20:

Find the number of terms of the geometric sequence ( 2 3 , 6 9 , 2 0 7 , … ) for which the sum is equal to 2 783.

Q21:

Find the sum of the geometric sequence ( 1 6 , − 3 2 , 6 4 , … , 2 5 6 ) .

Q22:

A gold mine produced 2,257 kg in the first year where production decreased by 1 4 % annually. Find the amount of gold produced in the third years and the total across all three years. Give the answers to the nearest kg.

Q23:

Find the sequence and the sum of the first five terms of an infinite geometric sequence, given the sum to infinity is 294, and the sum of the first and second terms is 4 4 1 2 .

Q24:

The table shows the number of bacteria in a laboratory experiment across five consecutive days. Two values are missing, but you know that the number of bacteria can be described by a geometric sequence. Calculate the average number of bacteria over the five days.

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