Question

1, 1.5, 2, 2.5, 3,... upto 16 terms,Find the sum of the first n terms of the following AP.as asked for.

Answer 1

a = 1

d = 0.5

n = 16

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

= 16 /2 [ 2× 1 + 15 × 0. 5]

= 8 ( 2 + 7.5)

= 8 × 9.5

= 4 × 19

= 76

Answer 2

Given A.P :

1 , 1.5 , 2 , 2.5 , 3 , ...upto 16 terms

First term ( a ) = 1 ,

Common difference (d)= a2-a1

d = 1.5 - 1 = 0.5

i ) Sum of n terms ( Sn )

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

Here ,

a = 1 , d = 0.5 , n = 16

S16 = 16/2[ 2×1 + ( 16-1)(0.5)]

= 8[ 2 + 15 × 0.5 ]

= 8[ 30 + 7.5 ]

= 8 × 37.5

= 300

S16 = 300

ii ) Sum of n terms ( Sn )

= n/2[ 2×1+(n-1)(0.5)]

= n/2[ 2 + 0.5n - 0.5 ]

= n/2[ 0.5n + 1.5]

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