Question

7 Find the average of the first 10 multiples
of 15.​

Answer 1

Answer:

Average of the first 10 multiples of 15 is 82.5

Step-by-step explanation:

We can solve it in 2 ways, according to the standard level,

Method 1

We need to find,

Average of the first 10 multiples of 15,

So,

Average = Sum of numbers/No. of numbers

Hence,

Average = (15 + 30 + 45 + 60 +............ + 135 + 150)/10

But,

30 = 2 × 15

45 = 3 × 15

So,

[(1 × 15) + (2 × 15) + (3 × 15) + .......... + (9 × 15) + (10 × 15)]/10

Taking 15 common,

15(1 + 2 + 3 + 4 +........... + 9 + 10)/10

Now,

Adding from 1 to 10 we get,

1 + 2 + 3 +........ + 9 + 10 = 55

So,

Av. = 15(55)/10

Av. = 825/10

Av. = 82.5

Method 2

We can also use A.P here,

We must first find the sum of 15, 30, 45,......., 135, 150.

So,

a (1st term) = 15

l (last term) = 150

n (no. of terms) = 10

Then,

Sn = (n/2)(a + l)

S(10) = (10/2)(15 + 150)

S(10) = 5(165)

S(10) = 825

So,

Average = Sum/No. of numbers

Av. = 825/10

Av. = 82.5

Hence,

Average of the first 10 multiples of 15 is 82.5.

Hope it helped and believing you understood it........All the best