Question

Find the sum of following A.P 1,3,5,7,............,199

Answer 1

Hiii !

First term = a₁ = 1

Second term = a₂ = 3

Common difference = d = a₂- a₁ = 3 - 1 = 2

Last term = an = 199

an = a+ (n-1)d
199 = 1 + (n-1)2
198 = (n-1)2
198/2 = n - 1
99 = n - 1
n = 100

No: of terms = n = 100

Sum = Sn

Sn = n/2 [a + an]
     = 100/2 [ 1 + 199]
     = 50 [ 200]
     = 10000

Sum = 10000
      

Answer 2

Heya,

Given:-

a = 1

d = 3-1

=2

an = 199

an = a + (n-1)d

⇒ 199 = 1+ (n-1) 2

⇒198 = (n-1)2

⇒n-1 = 99

⇒n=100

Sn = n/2 [2a+(n-1)d]

= 50[ 2 + (100-1) 2]

= 50 [2 + 198]

= 50 × 200

= 10000

Hope it helps u..................