HOW TO FIND THE SUM OF TERMS WHICH ARE MULTIPLES BETWEEN TWO NUMBERS

How to Find the Sum of Terms Which are Multiples Between Two Numbers ?

To find the sum of the series, we use the formula given below.

Sn  =  (n/2) [a + l] (or)

Sn  =  (n/2) [2a + (n - 1)d]

How to Find the Sum of Terms Which are Multiples Between Two Numbers

Question 1 :

If the sum of the first n terms of an AP is 4 n - n²  what is the first term (that is S)? what is the sum of first two terms?what is the second term? similarly find the 3rd,the 10th and the nth terms.

Solution :

Sn  =  4 n - n²

Sum of first two terms  =  4

 n = 1   = 4 (1) - (1)²    = 4 - 1 = 3first term = 3 S n = 4 n - n²n = 2   = 4 (2) - (2)²    = 8 - 4 = 4

To find the second term, we have to subtract the sum of two terms from first term

=  4 - 3  =  1

Second term  =  1

a =  a+2d

d = second term - first term  =  1 - 3  =  -2

a3 =  3 + 2(-2)  =  3 - 4 = -1

a10  =  a + 9 d

=  3 + 9(-2)

= 3 - 18

= -15

Question 2 :

Find the sum of first 40 positive integers divisible by 6.

Solution :

The positive integers which are divisible by 6 are

6, 12, 18,...........

6 + 12 + 18 + ...........

a = 6, d = 12 - 6  =  6, n = 40

Sn  =  (n/2) [ 2 a + (n - 1) d]

S40  =  (40/2) [2(6) + (40-1) (6)]

=  20 [12 + 39(6)]

=  20 [12 + 234]

=  20 [246]

=  4920

Question 3 :

Find the sum of first 15 multiples of 8.

Solution :

first 15 multiples of 8 are

8, 16, 24,................

8 + 16 + 24 + ...........

a = 8         d = 16 - 8       n = 15

= 8

Sn  =   (n/2) [ 2 a + (n - 1) d]

S15 = (15/2) [2(8) + (15-1) (8)]

=  (15/2) [16 + 14(8)]

=  (15/2) [16 + 112]

=  (15/2) [128]

=  15 [64]

=  960

After having gone through the stuff given above, we hope that the students would have understood, how to find the sum of terms which are multiples between two numbers.

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