In a sequence of numbers in which each term is two more than the prece

Given sequence is an arithmetic progression ( since each new term is two more than the previous). We need to find the fourth term.

St (1) Insufficient! as we do not have any info about the # of terms, we cannot be certain where the sequence begins.

St (2) Sufficient! given the first term and the difference between two terms we can determine any term of the sequence as it is an AP.

Hence Option (B) is our choice!

Best,
GLadi


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\(S_n = S_n-1 + 2\)

Given that we don't know how many terms are there? it could be that the last term is actually 5 and it could be 100.. so we cannot figure out anything specific.

Insufficient.

Knowing \(S_2 = S_1 + 2 = 2 + 2 = 4\)

we can solve for it and find \(S_4 = S_3 + 2 = S_2 + 2 + 2 = S_1 + 2 + 2 + 2 = 2 + 2 + 2 + 2 = 8\)

B is sufficient.

Statement 1: Last term is 90. We do not have any information regarding first term and how many terms are there? Insufficient

Statement 2: First term is 2 with this we can calculate the fourth term as it is given that each term is two more than the preceding term. Hence Sufficient

B is the right answer

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FORMULA FOR FINDING # OF TERMS

\(x_n = a+d (n-1)\)

\(n\) = # of term
\(a\) = first term
\(d\) = distance between terms

As per statement ONE the last term is 90, however it is not sufficient because we dont know the first term: it can be any number.

As per statement TWO the first term is 2. Since we know as well distance between terms. we can get the FOURTH term

\(x_4 = 2+2 (n-1)\)

\(x_4 = 2+2n-2\)

\(x_4 = 2n\) plug in 4

\(x_4 = 2*4\)

\(x_4 = 8\)

B

Target question: What is the value of term_4?

Statement 1: The last term is 90.
We have no idea how many terms there are in the sequence. So, the last term could be term_5 or term_9 or term_12 or . . .

Consider these two possible cases:
Case a: The last term is term_6. In this case, term_6 = 90, term_5 = 88, term_4 = 86, term_3 = 84....etc. So, the answer to the target question is term_4 = 86
Case b: The last term is term_5. In this case, term_5 = 90, term_4 = 88, term_3 = 86 ....etc. So, the answer to the target question is term_4 = 88
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The first term is 2.
If term_1 = 2, then: term_2 = 4, term_3 = 6, term_4 = 8, . .. etc
The answer to the target question is term_4 = 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

(1) We know increment but we don't know the first term. Insufficient

(2) We know increment and the first term. sufficient.

(1) Gives no information on the total number of terms, hence cannot determine the 4th term. Insufficient.

(2) 1st term = 2, therefore 2nd term = 4, 3rd term = 6, and 4th term = 8. Sufficient.

Hence, B.

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