Question

Which term of arithmetic sequence 2,6,10 .....is 102?

Answer 1

Answer :

26th

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 : 2 , 6 , 10 , . . .
• To find : If a(n) = 102 , then n = ?

Clearly , we have

First term ,a = 2

Common Difference , d = 6 - 2 = 4

nth term , a(n) = 102

Also ,

We know that , the nth term of an AP is given by ;

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

Thus ,

=> 102 = a + (n - 1)d

=> 102 = 2 + (n - 1)•4

=> 4•(n - 1) = 102 - 2

=> 4•(n - 1) = 100

=> n - 1 = 100/4

=> n - 1 = 25

=> n = 25 + 1

=> n = 26

Hence ,

102 is the 26th term of the given AP .

Answer 2

Step-by-step explanation:

Given : 2,6,10,...

To find: Which term of AP is 102?

Solution:

Tip:

General term of A.P. is

$\bf a_n = a + (n - 1)d$

Step 1: Write a, d and nth term

$a = 2$

$b = 6 - 2 = 4$

$a_n = 102$

Step 2: Put the values in the formula

$102 = 2 + (n - 1)4$

$102 - 2 = 4(n - 1)$

or

$100 = 4(n - 1)$

or

$(n - 1) = \frac{100}{4}$

or

$n - 1 = 25$

or

$n = 25 + 1$

$\bf n = 26$

Final answer:

26th term of arithmetic sequence 2,6,10...is 102.

Hope it helps you.

To learn more on brainly:

The sum of first n terms of an arithmetic progression is 210.and sum of its first n-1 terms is 171.if the first term is ...

https://brainly.in/question/12304646

find the number of terms of the AP -12, -9, -6 ... , 21. If 1 is added to each term of this AP, then find the sum of ...

https://brainly.in/question/8420712