Question

The value of 1 +3+5+7+....+ 37 is equal to?
(Only this information is given please solve it)

Answer 1

a=1
l=37
d=3-1=2
tn=a+(n-1)d
37 =1+(n-1)2
36=2n-2
n=19
sn=n/2(a+l)
=19/2(1+37)
=19/2×38
=361

Answer 2

The value of 1 + 3 + 5 + 7 + ..... + 37 = 324

Given:

1 +3+5+7+....+ 37

To find:

The value of 1 +3+5+7+....+ 37

Solution

Given number sequence 1 +3+5+7+....+ 37 is a AP

Here, first term a = 1

Common difference d = 3-1= 2

last term = 37

Let 37 be the nth term of AP

As we know nth term of AP  = a +(n-1)d

=> a + (n-1)d = 37

=> 1 + (n-1)2 = 37

=> 1 +2n -2 = 37

=> 2n = 36

=>  n = 18

Number of terms in AP = 18

As we know sum of n terms in AP = n/2 [ 2a+(n-1)d ]

= 18/2 [ 2(1) +(18-1)2 ]

= 9 [ 2 + (17)2 ]

= 9 [ 2 + 34 ]

= 9 [ 36 ]

= 324

Therefore,

The value of 1 + 3 + 5 + 7 + ..... + 37 = 324

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