What is the sum of the 20th and 21st terms in the sequence

Question

What is the sum of the 20th and 21st terms in the sequence 1, 3, 9, 27... where each term is 3 times the preceding term?

4 * 3^19

10 * 3^19

4 * 3^20

10 * 3^20

3^39

ncp · Answer

t20=3^19
t21=3^20

Sum = 3^19(1+3) = 4*(3^19)

A.

soxy_topacio · Answer

I don't have my head on today, please explain how you got to this step.

alfyG · Answer

I agree with the above answer:

1,3,9,27,..., 3^n, for n is great or equal to 0 

the 20th term is 3 ^19 since we started with n=0
the 21th term is 3^ 20

3^19 + 3^20 => take out common factor => 3^19 + 3*3^19

= 3^19(1 + 3) = 3^19 * 4

querio · Answer

A) 

If a term is found by multiplying the previous term by a facto (r), then this is a Geometric Progression. 
The Nth term of a GP is defined as-> 

 Nth = a * r^(N-1) --- a: first term; r: factor; 

In this example, we have the following values:
a=1
r=3
N=20 and 21

So, when N=20 the term is found by the formula 1*3^(20-1)=3^19
and when N=21 the term is 1*3(21-1)=3^20

The sum of the terms is 3^19+3^20 = 3^19 (1+3^1) = 4 * 3^19

alfyG · Answer

querio you are right.. but you do not need to introduce a formula for this type of problem; the general form can readily be derived; that is 3^n

I think the key to GMAT success is to solve these types of problems with as little 'external resources' as possible.

KillerSquirrel · Answer

I agree with alfyG - if you are too busy writing down a formula, you are limiting yourself. Try to apply the formula  after   you thought about the problem and you think you know the right way to solve it, and only if you must ! sometimes more (math) is less (time).

goalsnr · Answer

term value
1 1 = 3^0
2 3 = 3^1
3 9 = 3^2

20 3 ^19
21 3^20


Sum = 3 ^19 + 3^20
 =3 ^19 (1+3)
 = 4*(3 ^19 )

Swagatalakshmi · Answer

T(n) = 3^(n-1)

T(20) + T(21)
=3^19 + 3 ^20
=4* 3^19

javed · Answer

the series is 1,3,9,27,... i.e 1,3^n where n=1,2,3, . therefore 20th term = 3^19 and 21st term= 3 ^20.
Now adding them we get 3^19(3+1)= 4*3^19. So the answere is A.

Javed.

Cheers!

querio · Answer

I agree. However, I wouldn't say either "don't apply the formula before thinking about the problem". My advice would be to try all the different methods, select the one that you are more comfortable with and then master it! Bear in mind that energy management is crucial on the Gmat, so if it takes you a couple of extra seconds to solve a problem applying a formula but you consumed less energy by doing so, then apply the formula! The same will apply if you would like to follow the "pure math" way. Summarizing, when selecting a method to solve a problem don't consider only the TIME YOU SAVE, but also the ENERGY YOU SPEND!
Cheers,
Fede

ywilfred · Answer

this is a geometric progression series where each term is ar^n where a is 1, r is 3 and n is the term.

so 20th term = 3^20 and 21st term is 3^21

The sum is 3^20(1+3) = 4*3^20

nick_sun · Answer

But what about the first term "in the sequence  1 , 3, 9, 27....."?

querio · Answer

The first term (n=1, a=1, r=3) = 1*3^(1-1) = 1
Scond term (n=2, a=1, r=3) = 1*3^(2-1) = 3
and so on...

KillerSquirrel · Answer

I completely agree with your comment, Querio, but what i meant to say is that you have the right way to solve GMAT problems (i.e every solution in the OG is the right way) but you have the fast way to solve those problems (i.e pluging in). in either cases knowing and understanding the right way is crucial in geting good GMAT scores, even if you are using the fast way, but in most cases you don't need to use formulas to solve a problem. Only to understand the logic behind it. "You can't get a Nobel Prize for solveing a GMAT problem"

What is the sum of the 20th and 21st terms in the sequence

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