Question

18.Find the sum of the first 30 positive integers divisible by 6.​

Answer 1

Step-by-step explanation:

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . . , 180.

The first term a = 6

The common difference d = 6

Total number of terms n = 30

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 30/2 x (6 + 180)

= (30 x 186)/ 2

= 5580/2

6 + 12 + 18 + 24 + 30 + 36 + 42 + 48 + 54 + 60 + . . . . + 180 = 2790

Therefore, 2790 is the sum of first 30 positive integers which are divisible by 6.

Answer 2

Step-by-step explanation:

To find:sum of the first 30 positive integers divisible by 6.

By using the formula,

Sn= n/2{2a+(n-1)d}. where ,,

Sn is the sum of Numbers

n is number of terms

a is first term

d is the common difference

So the first integer(A1) divisible by 6 is 6 itself.

A2=12

hence d=12-6= 6

n=30 (given)

So by substituting the values in the formulae.

Sn=30/2 {2×6+ (30-1) × 6}

=15 (12 + 29×6 )

=15( 12+174 )

=15 (186)

=2,790

Hence,the sum of the first 30 positive integers divisible by 6 is 2,790.

Hope this helps