Question: In a sequence 1, 2, 4, 8, 16, 32, ... each term after the first is twice the previous term. What is the sum of the 16th, 17th and 18th terms in the sequence ?

1. 2^18
2. 3(2^17)
3. 7(2^16)
4. 3(2^16)
5. 7(2^15)

Correct Answer: (E)

Solution and Explanation:
Approach Solution 1:

The problem statement informs that:

Given:

• In a sequence 1, 2, 4, 8, 16, 32, ... each term after the first is twice the previous term

Find Out:

• The sum of the 16th, 17th and 18th terms in the sequence

Since each term after the first is twice the previous term, therefore, we can say,

a1=2^0=1;
a2=2^1=2;
a3=2^2=4;
…
an=2^(n−1);

Therefore, a16 + a17 + a18= 2^15 + 2^16 + 2^17 = 2^15(1+2+4) = 7∗ 2^15.
Hence, the sum of the 16th, 17th and 18th terms in the sequence = 7∗ 2^15.

Approach Solution 2:

The problem statement informs that:

Given:

• In a sequence 1, 2, 4, 8, 16, 32, ... each term after the first is twice the previous term

Find Out:

• The sum of the 16th, 17th and 18th terms in the sequence

We can derive the solution in the quickest and easiest way as follows:

As per the question, the 16th term = 2^15 (since 2^0 = 1).
Hence we require to find out 2^15+2^16+2^17.

Now, let’s take smaller numbers: 2^2+2^3+2^4 = 28 = 7*(2²) (which is regarded as the first term), Hence it can be inferred that 7*(2^15) will be the right answer choice.

Approach Solution 3:

The problem statement informs that:

Given:

• In a sequence 1, 2, 4, 8, 16, 32, ... each term after the first is twice the previous term

Find Out:

• The sum of the 16th, 17th and 18th terms in the sequence

As per the condition of the question,
1st term, --------------------------------------, 6th term ,…
can be written as : 1 ,(2) ,(2*2),(2*2*2),(2*2*2*2) , (2*2*2*2*2),...

which again can be derived as : 1 , 2^1, 2^2 , 2^3 , 2^4 , 2^5 ,...

Therefore, we can infer,
16th term : 2^15 ---(1)
17th term : 2^16 ---(2)
18th term : 2^17 ---(3)

By summing up the equation (1),(2) & (3)
2^15 + 2^16 + 2^17 = 2^15(1+ 2^1 + 2^2) = 2^15 ( 1+2+4) = 2^15 (7)

Hence, the sum of the 16th, 17th and 18th terms in the sequence = 2^15 (7).

“In a sequence 1, 2, 4, 8, 16, 32, ... each term after the first is twice''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions facilitate the candidates’ skills to analyse information and crack numerical sums. GMAT Quant practice papers enable the candidates to improve their mathematical knowledge as it cites different sorts of numerical problems.

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