Question: What is the sum of 7 terms of a 'geometric progression' whose first term is 1 and the 4th term 27?
- 1093
- 2186
- 3279
- 4372
- 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.
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