Question

The fortieth odd number is

81
39
79
41
and the sum of the first forty odd numbers is
80
1600
158
6241

Answer 1

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

Answer 2

Answer: 1) Third Option is correct.

2) Second Option is correct.

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* 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=(n)/(2)(2x+(n-1)d)\\\\S_(40)=(40)/(2)(2* 1+(40-1)2)\\\\S_(40)=20(2+39* 2)\\\\S_(40)=20(2+78)\\\\S_(40)=20* 80\\\\S_(40)=1600`

Hence, Second Option is correct.