If an=n^5+n/10, what is the value of a11?

Question

If  a_n=n^5+\frac{n}{10} , what is the value of  a_{11} ?

A. 161,052.1
B. 161,051.1
C. 121,121
D. 61,052
E. 14,642.1

Solve without actual calculations.

pushpitkc · Answer

We need to find the value of  a_n=n^5+\frac{n}{10}  when n=11?

a_n=11^5+\frac{11}{10} 
=  \frac{{11^5*10 + 11}}{10} 
=  \frac{{11(11^4*10 + 1)}}{10}

This is of the form 1.1(xxxxx1) = xxxxx2.1
 Option A is the only answer choice similar to this

Leo8 · Answer

It has to be A..

11^n = ......1 ( the digit at unit place will always be 1) 
11/10 = 0.1

so the sum must = ....2.1

only A & E have it but option E is very less as 10^ 5 = 100,000 > 14,642

so A is the answer

Smokeybear00 · Answer

\frac{11}{10}  = 1.1

11^5  will always have a 1 in the units place so 1+1.1=2.1

A or E

11^5  is like  10^5 , so five zeros 1xx,xxx

Answer A

shashankism · Answer

a11= 11^5 +11/10 = 11^5 +1.1

Since 11^n has last digit as always 1. So 11^5 +1.1 will be of the form .....2.1

Hence We can rule out options B,C,D

Now we need to select from options A and E.

Now 11^5 > 10^5 =100000
Since 14642.1 < 10^5 we can rule out option E.

So Option A is correct.

A nice question which can be solved in 30 second without much calculation..

rulingbear · Answer

Yes, best is to solve without calculation by noticing that the second part of the question which is \frac{11}{10} =1.1 eliminate D
Next is to know that the unit digit is 2 i.e, the last digit of n^5 is 1, so the number ends with 2.1 (1+1.1). Now answer is between A and E
 Last it to use divisibility by 11  and both options A and E minus 1 are divisible by 11, but A yields 11^4 and E, 11^3.  Hence, A . Alternatively, we can deduce that  11^5 is (121^2)11  definitely more like A than E.  Hence, A.

Spartan85 · Answer

Answer:

11^5 + 11/10

11/10 =1.1

(Choice - 1.1 ) should be divisible by 11

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If an=n^5+n/10, what is the value of a11?

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If an=n^5+n/10, what is the value of a11?

Prep Toolkit

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