Question

Find the sum of all number
divisible by 5 between 70 and 400
​

Answer 1

Answer:

15745 or 1.5745×10^4

Step-by-step explanation:

Let's form an A.P. in order to solve the problem

a1 = 70

an = 400

{common difference is 5 because , it's given that the numbers divisible by 5}

d = 5

a2 = a +d

a2 = 70 +5 = 75

an = a+(n-1)d

400 = 70+(n-1)5

400 = 70+5n-5

70+5n-5 = 400

5n = 400 -70 +5

5n = 335

n = 335 /5

n = 67

So, 67 terms (numbers) are divisible by 5 between 70 amd 400

Now, solving the sum

Sn = n/2 {2a+(n-1)d} or

Sn = n/2 (a1 + an)

S67 = 67/2 (70+400)

S67 = 67/2 (470)

S67 = 67×470 /2

S67 = 67×235

S67 = 6.7×2.35×10^3

S67 = 15.745×10^3 = 1.5745×10^4

or

S67 = 15745

So, the sum of all the numbers divisible by 5 between 70 amd 400 is 15745 or 1.5745×10^4