Question

1/3,4/3,7/3,10/3, .... upto 18 terms,Find the sum of the first n terms of the following AP.as asked for.

Answer 1

a = 1/3

d = 4/3 - 1/3 = 3 /3 = 1

Now,

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

= 18 /2 [ 2/3 + 17 × 1]

= 9 ( 2/3 + 17)

= 9 × 53 / 3

= 3 × 53

= 159

Answer 2

Given A.P:

1/3 , 4/3 , 7/3 , 10/3 ,...upto 18terms

First term ( a ) = 1/3

Common difference (d)=a2-a1

=> d = 4/3 - 1/3

=> d = 2/3

i ) Sum of n terms ( Sn )

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

S18 = 18/2[ 2(1/3)+ ( 18-1 )(2/3)]

= 9[ 2/3 + 34/3 ]

= 9 ×( 36/3 )

= 9 × 12

= 108

S18 = 108

ii ) Sum of n terms ( Sn )

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

= n/2[ 2(1/3) + ( n -1 )( 2/3 ) ]

= n/2 [ 2/3 + 2n/3 - 2/3 ]

= ( n/2 )( 2n/3 )

= n²/3

Sn = n²/3

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