Question

1st term is 10 and 20th term is 60.find the common difference of sum of the 20 terms​

Answer 1

Step-by-step explanation:

Given :-

1st term is 10 and 20th term is 60.

To find:-

Find the common difference of sum of the 20 terms ?

Solution :-

First term of an AP = (a) = 10

We know that

If a is the first term and d is the common difference then the general term an = a+(n-1)d

Now,

Given that

20th term = 60

=> a 20 = 60

=> a+(20-1) d = 60

=> a+19d = 60

=> 10+19d = 60

=> 19d = 60-10

=> 19d = 50

=> d = 50/19

Common difference = 50/19

We know that

The sum of first n terms in an AP

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

On Substituting these values in the above formula then

=> Sum of 20 terms

=> S 20 = (20/2)[2(10)+(20-1)(50/19]

=> S 20 = (10)[20+19(50/19)]

=> S 20 = (10)(20+50)

=> S 20 = (10)(70)

=> S 20 = 700

Answer:-

Common difference of the given AP = 50/19

Sum of 20 terms of the given AP = 700

Used formulae::

• If a is the first term and d is the common difference then the general term an = a+(n-1)d
• The sum of first n terms in an AP
• = Sn = (n/2)[2a+(n-1)d]