Question

In an old story, a man puts 2 grains of rice on the first space of a chess board. He puts 4 grains on the second space, 8 grains on the third space, and so on. Write and evaluate an expression with exponents to find how many grains of rice the man puts on the tenth space.

Answer 1

GEOMETRIC PROGRESSIONS

Heya !

In the story we got to know that the man put 2 grains of rice in first space of a chess board ,

4 grains on the second space of chess board

And 8 on the 3rd one and so on ,

So on noticing carefully , we see a Geometric Progression formed here ,

With first term a = 2
and common difference = 2

Now , we have to find the number of grains on the old man puts on the 10th space ,

I.e we have to find the 10th term of the given Geometric Progression ,

$T10 = a {r}^{9} \\ T10= 2 \times {2}^{9} \\ \\ T10= {2}^{10} = 1024 \: \: \: \: \: \: \: Ans.$

Answer 2

We know that
a1----------> grains of rice in the first square
a1=2
n------------> space ubication
the expressions  is
 an=a1^n----------> an=2^n

for the the tenth space  n=10
an=2^10---------> an=1024 grains of rice

the answer is
1024 grains of rice