Question

 Is multiples of 5 from below 100 natural numbers is Arithmetic Progression? Find its sum.​

Answer 1

yes

multiples of 5 below 100 natural numbers is A.P.

as d = 5 is constant

the given A.P. is - 5,10,15,_ _ _ _,95

here

a = 5 , d = 5 ,tn = 95

we have ,

tn = a + (n-1)d

95= 5 + (n-1)× 5

95-5 = 5n -5

90 + 5=5n

95/5 = n

n = 19

Now,

Sn = n/2(a+ tn)

= 19/2(5+95)

= 19/2 × 100

= 19 × 50

= 950

hope it helped

Answer 2

5, 10,15,20,25.......95

It's a sequence

d=5

Since the difference is constant

It's an A.P.

a=5. d=5 tn=95

tn=a+(n-1)d

95=5+(n-1)5

90=5n-5

95=5n

n=95/5

n=19

Now,

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

S19=19/2[2*5+(19-1)5]

S19 =19/2*(10+95-5)

=19/2*100
=19*50
=950

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