Verified Answer :

serenakmays

The fortieth odd number is 
79
and the sum of the first forty odd numbers is 
1600

Answer: 1) Third Option is correct.

2)  Second Option is correct.

Step-by-step explanation:

Since we have given that

odd numbers are as follows:

1, 3, 5, .........................

so, first term = a = 1

d = common difference = 3-1=2

n =  number of terms = 40

As we know that it forms an "Arithmetic Progression ":

\(a_n=a+(n-1)d\\\\a_n=1+(40-1)2\\\\a_n=1+39\times 2\\\\a-n=1+78\\\\a_n=79\)

so, the fortieth odd number is 79.

Hence, Third Option is correct.

Now, we need to find the first forty odd numbers :

As we know the formula :

\(S_n=\frac{n}{2}(2x+(n-1)d)\\\\S_{40}=\frac{40}{2}(2\times 1+(40-1)2)\\\\S_{40}=20(2+39\times 2)\\\\S_{40}=20(2+78)\\\\S_{40}=20\times 80\\\\S_{40}=1600\)

Hence, Second Option is correct.  

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