The infinite sequence a1, a2, …, an, … is such that a1=2

the sequence is repeating after each 4 terms.

i.e 2,-3,5,-1 ,2,-3,5,-1 ,2,-3,5,-1 ,2,-3,5,-1 ....till 97th term.

Now (2,-3,5,-1 ),(2,-3,5,-1) ,(2,-3,5,-1 ),......................(2,-3,5,-1) ,1

97 = 24 *4 + 1

Means 24 similar like (2,-3,5,-1 ) and one more that is first term of the series

the sum of the first four term is = 3


Hence sum is 24*3 + 2 = 74

Hence answer is B.

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Nice one, a pattern problem with an addition twist.

a1 = 2, a2 = -3, a3 = 5, a4 = -1
What an = a(n-4) means that from a5 onwards, every number in the sequence will be equal to 4 numbers preceding that number. Therefore, a5 = a1 = 2, a6 = a2 = -3,...

Notice that this is a 4-element set pattern. If we sum a1-a4, we get 3. What is the closet multiple of 4 to 97 - 96! So, there are 24 such complete sets. Added to that is 97th number, which is first in the sequence = 2. So, we get (24 x 3) + 2 = 74 -> B

\(a_1 = 2\)

\(a_2 = -3\)

\(a_3 = 5\)

\(a_4 = -1\)

\(a_5 = a_{(5-4)} = a_1 = 2\)

\(a_6 = a_{(6-4)} = a_2 = -3\)

\((a_1 + a_2 + a_3 + a_4) = (a_5 + a_6 + a_7 + a_8) = (a_9 + a_{10} .....)\) and so on

Addition upto \(a_{96}\) is repeated 24 times

\((a_1 + a_2 + a_3 + a_4) = 2 - 3 + 5 - 1 = 3\)

\(a_1 + a_2 + a_3 + ........ + a_{96} = 3 * 24 = 72\)

\((a_1+a_2+a_3+ ........ + a_{96}) + a_{97} = 72 + 2 = 74\)

Answer = B

We are given that a(1) = 2, a(2) = -3, a(3) = 5, and a(4) = -1.

Since a(n) = a(n-4), we see that:

a(5) = a(5-4) = a(1) = 2,

a(6) = a(6-4) = a(2) = -3,

a(7) = a(7-4) = a(3) = 5,

and a(8) = a(8-4) = a(4) = -1

As we can see, the terms repeat themselves in a cycle of 4.

Since the sum of the terms a(1) to a(4) inclusive is [2 + (-3) + 5 + (-1)] = 3, the sum of a(5) to a(8) will also be 3, as will the sum of a(9) to a(12), etc.

We see from each “grouping” of 4 numbers, we have a sum of 3, and from 1 to 96 inclusive there are:

(96 - 4)/4 + 1 = 92/4 + 1 = 24 such groupings. Thus, the sum of those 24 groupings is 24 x 3 = 72.

We must also add the value of a(97), which equals 2.

Thus, the sum of the first 97 terms is: 24 x 3 + 2 = 72 + 2 = 74.

Answer: B

Can anyone provide me with a quality information(website, youtube etc) on GMAT sequences. I cant seem to decode such sort of questions

12. Sequences

• Theory
  Math : Sequences & Progressions
  
  • Questions
    Special Numbers and Sequences Problems
    DS Questions
    PS Questions

For ALL other subjects check Ultimate GMAT Quantitative Megathread

(I pointed you to this topic multiple times)

Hope it helps.

Hi can you help understand why can't we use the formula here N(A1+AN)/2 ? Thanks

The formula you quote, is for evenly spaced sets (aka arithmetical progression), and cannot be applied to all sequences. The sequence at hand is 2, -3, , 5, -1, ... As you can see this is not an arithmetic progression, so you cannot use that formula.

Check links below for more.

12. Sequences

• Theory
  Sequences Made Easy - All in One Topic!
  Math : Sequences & Progressions
  Time to Tackle Geometric Progressions!
  
  • Questions
    Special Numbers and Sequences Problems
    DS Questions
    PS Questions

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.

Hello,

So this progression is neither an AP or GP correct? and thus the equations for the sum do not apply

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