Question

find 100th term of AP 8,13,18..... also find sum of 100 terms​

Answer 1

Answer:

s100=25550

Step-by-step explanation:

$sn = 100 \div 2(2 \times 8 + 100 - 1 \times 5) \\ = 25550$

Answer 2

Answer :

S(100) = 25550

Note :

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ If a1 , a2 , a3 , . . . , an are in AP , then

a2 - a1 = a3 - a2 = a4 - a3 = . . .

★ The common difference of an AP is given by ; d = a(n) - a(n-1) .

★ The nth term of an AP is given by ;

a(n) = a + (n - 1)d .

★ If a , b , c are in AP , then 2b = a + c .

★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .

or S(n) = (n/2)×(a + l) , l is the last term .

★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .

Solution :

• Given AP : 8 , 13 , 18 , . . .
• To find : S(100) = ?

Here ,

The given AP is 8 , 13 , 18 , . . .

Clearly ,

First term , a = 8

Common difference , d = 13 - 8 = 5

No. of terms , n = 100

Now ,

We know that , the sum of n terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .

Thus ,

=> S(100) = (100/2)×[ 2a + (100 - 1)d ]

=> S(100) = 50×(2a + 99d)

=> S(100) = 50×(2•8 + 99•5)

=> S(100) = 50×(16 + 495)

=> S(100) = 50×511

=> S(100) = 25550

Hence S(100) = 25550 .