Question

find the value of 16+17+18+....+75​

Answer 1

16+17+18...+75

this series in AP

a= 16

d = 1

an = 75

an = a+(n-1)d

75 =16+(n-1)1

59= n-1

n = 60

Sn = 60/2 [ 16+75]

= 30× 91

= 2730

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Answer 2

Given :  16+17+18+....+75​

To Find : Sum

Solution:

16+17+18+....+75​  

one way

= ∑ n ( 1 to 75)  -   ∑ n ( 1 to 15)

∑n = n(n + 1)/2

= 75(76)/2 - 15(16)/2

= 75(38) - 15(8)

= 15( 190 - 8)

= 15 ( 182)

=  2730

Another way

16+17+18+....+75​  

This is an AP

a = 16  d  = 1  , L = 75

75 = 16 + (n - 1) 1

=> n = 60

Sum = (n/2)(a + L)

= (60/2)(16 + 75)

= 30(91)

= 2730

value of 16+17+18+....+75​ = 2730

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