Question

what is the difference between the sum of first 10 terms and next 10 terms of the arithmetic sequence 3,9,15...​

Answer 1

Answer:

600

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

The AP is 3,9,15...

To find :-

What is the difference between the sum of first 10 terms and next 10 terms of the arithmetic sequence 3,9,15... ?

Solution :-

Given AP is 3,9,15,...

First term (a) = 3

Common difference (d) = 9-3 = 6

We know that

The general form of an AP is a1,a2,a3,...

= a,a+d,a+2d,....

We know that

The nth term of an AP = an = a+(n-1)d

The sum of first n terms of an AP is

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

The sum of first 20 terms of the given AP

= a1+a2+a3+...+a20

S20 = (20/2)[2(3)+(20-1)(6)]

=> S20 = 10(6+19(6))

=> S20 = 10(6+114)

=> S20 = 10(120)

=> S20 = 1200

and

The sum of first 10 terms of the given AP

= a1+a2+a3+...+a10

S10 = (10/2)[2(3)+(10-1)(6)]

=> S10 = 5(6+9(6))

=> S10 = 5(6+54)

=> S10 = 5(60)

=> S10 = 300

and

The sum of next 10 terms = Sum of first 20 terms - Sum of the first 10 terms

=> 1200-300

=> 900

The difference between the sum of first 10 terms and the sum of next 10 terms

=> 900-300

=> 600

Sum of first 10 terms - Sum of next 10 terms

=> 300-900 = -600

or

Sum of next 10 terms - Sum of first 10 terms

=> 900-300

=> 600

Answer:-

Sum of first 10 terms - Sum of next 10 terms = -600

Sum of next 10 terms - Sum of first 10 terms = 600

Used formulae:-

• The general form of an AP is a1,a2,a3,...
• = a,a+d,a+2d,....
• The nth term of an AP = an = a+(n-1)d
• The sum of first n terms of an AP is
• Sn = (n/2)[2a+(n-1)d]