Question: What is the sum of 7 terms of a 'geometric progression' whose first term is 1 and the 4th term 27?

1. 1093
2. 2186
3. 3279
4. 4372
5. 2231

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

The problem statement asks to find the sum of 7 terms of a 'geometric progression' whose first term is 1 and the 4th term 27.
If the 4th term is 27, \(ar^3\) = 27....1∗ \(r^3\) = 27....r = 3
Sum of first n terms of a \(GP = a(r^n-1)/(r-1)\)

Therefore, by putting the value we get:
=\( 1(3^7-1)/(3-1)\)
= (2187−1)/2
= 2186/2
=1093

Therefore, the sum of 7 terms of a 'geometric progression' = 1093

Approach Solution 2:

The problem statement asks to find the sum of 7 terms of a 'geometric progression' whose first term is 1 and the 4th term 27.
In a geometric sequence, we find the next term by multiplying the previous term by a constant.
If the first term is a, and our constant is r, then the second term is ar, the third is ar^2, the fourth is ar^3, and so on.
Therefore, here if the first term is 1, and the fourth is 27, then r^3 = 27 and r = 3.
Hence the first seven terms are 1, 3, 9, 27, 81, 243, and 729.
Therefore, by adding all these seven terms we can get the sum of seven terms.
Thus, the sum of 7 terms = 1+ 3 + 9 + 27 + 81 + 243 + 729 = 1093
Hence, the sum of 7 terms of a 'geometric progression' = 1093

Approach Solution 3:

The problem statement asks to find the sum of 7 terms of a 'geometric progression' whose first term is 1 and the 4th term 27.
As per the condition of the question, it is given that,
a =1, \(a_4\) = 27
Therefore, we can say:
\(ar^3/a = 27/1\)

Hence, r = 3

Therefore, the Sum of the first 7 terms−
\(S_7 = a(r^7-1)/(r-1)\)

Therefore, by plugging the value we get:
=> \(S_7 = 1(3^7-1)/(3-1)\)

By simplifying we get:
=>\( S_7 = 1(2187−1)/2\)

By further simplifying we get:
=> \(S_7 = 2186/2\)

Therefore, \(S_7\) =1093
Hence, the sum of 7 terms of a 'geometric progression' = 1093.

“What is the sum of 7 terms of a 'geometric progression' whose first”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “501 GMAT Question”. The GMAT Problem Solving questions demand the candidates to have basic knowledge of math in order to solve quantitative problems. GMAT Quant practice papers enable the candidates to practice multiple questions that will help them to enhance their mathematical understanding.

Suggested GMAT Problem Solving Samples

• If the Tens Digit x and the Units Digit y of a Positive GMAT Problem Solving
• ABCD is a Trapezium, in which AD and BC are Parallel. If the Four Sides GMAT Problem Solving
• If 9^(x−1/2) –2^(2x–2) = 4^x – 3^(2x–3), then What is the Value GMAT Problem Solving
• Solve for x: 0<|x|-4x<5 = ? GMAT Problem Solving
• After the division of a number successively by 3, 4, and 7 GMAT Problem Solving
• If x^2−5x+6=2−|x−1|, what is the product of all possible values of x? GMAT Problem Solving
• What is the value of square root{25 + 10square root(6)} + square root{25 - 10square root(6)} GMAT Problem Solving
• In the figure shown above, what is the perimeter of parallelogram ABCD GMAT Problem Solving
• Which of the Following Represents the Range for all x Which Satisfy Inequality GMAT Problem Solving
• If the length of the longest chord of a certain circle is 10, what is GMAT problem solving
• A restaurant buys fruit in cans containing 3 1/2 cups of fruit each GMAT problem solving
• If 65 Percent of a Certain Firm’s Employees are Full-Time GMAT Problem Solving
• What is the Remainder When 3^24 is Divided by 5? GMAT Problem Solving
• A={1,2,3,4,5} is Given. If There are 1,2,…,n Subsets of A, Let A1 GMAT Problem Solving
• If 100 Centimetres = 1 Meter, then What is the Value of 100 Centimetre GMAT Problem Solving
• A Positive Integer x is Divisible by 2,3, and 5. What is The Smallest GMAT Problem Solving
• A Solid Metallic Cube is Melted to Form Five Solid Cubes Whose Volumes GMAT Problem Solving
• At a Supermarket, John Spent 1/2 of his Money on Fresh Fruits GMAT Problem Solving
• Positive Integer y is 50 Percent of 50 Percent of Positive GMAT Problem Solving
• A Pizza Can be Assembled from Given Choices, with Customer’s GMAT Problem Solving
• If y= 4 + (x - 3)^2, Then y is Lowest When x = GMAT Problem Solving
• What is the Value of w in Terms of x and y GMAT Problem Solving
• A New Flag is to be Designed with Six Vertical Stripes Using Some GMAT Problem Solving
• If x^2 + 1/x^2 = 4, What is the Value of x^4 + 1/x^4 GMAT Problem Solving
• A Dog Breeder Currently has 9 Breeding Dogs. 6 of the Dogs have GMAT Problem Solving
• The interior angles of a convex polygon are in arithmetic progression GMAT Problem Solving
• (x^2 + 2x - 8)/(x^2 - 6x + 8) = ? GMAT Problem Solving
• Which of the following is equal to the average (arithmetic mean) GMAT Problem Solving
• A trader has 400kg of rice, a part of which he sells at 36% GMAT Problem Solving
• A Number, x is Chosen at Random from the Set of Positive Integers Less GMAT Problem Solving
• Which of the following could be the area of an isosceles triangle with GMAT problem solving
• After M Students Took a Test, There was a Total of 64% GMAT Problem Solving
• Perimeter of a Triangle with Integer Sides is Equal to 15 GMAT Problem Solving
• PQRS is a Quadrilateral Whose Diagonals are Perpendicular to Each Other GMAT Problem Solving
• Which of the following is closest to (10.001)^2 ? GMAT Problem Solving
• A Train of Length L is Traveling at a Constant Velocity and Passes a Pole GMAT Problem Solving
• A circle is inscribed in an equilateral triangle of side 24 cm GMAT Problem Solving
• After 200 grams of water were added to the 24%- solution of alcohol GMAT Problem Solving
• Which of the following numbers is a perfect square? GMAT Problem Solving
• What is 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + 1/(6*7) GMAT Problem Solving
• What is the Remainder When2^99is Divided by 99? GMAT Problem Solving
• The first five numbers in a regular sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
• A Bar is Creating a New Signature Drink. There are Five possible Alcohol GMAT Problem Solving
• A Can Complete a Certain Job in 12 Days. B is 60% More Efficient than GMAT Problem Solving
• An Alloy of Gold,Silver and Bronze Contain 90% Bronze, 7% Gold and GMAT Problem Solving
• When Positive Integer n is Divided by 5, the Remainder is 1 GMAT Problem Solving
• A is Thrice as Efficient as B and Hence Takes 12 Days Less to Complete GMAT Problem Solving
• A Tank is Filled by Three Pipes with Uniform Flow. The First Two Pipes GMAT Problem Solving
• Each Person in a Group of 110 Investors Has Investments in Either GMAT Problem Solving
• Jim Travels the First 3 Hours of His Journey at 60 mph Speed GMAT Problem Solving