Question

Find first term of an AP whose last term is 205 and common
difference is 6 and number of term is 34.

Answer 1

Answér :

First term = 7

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) = a1 + (n - 1)d .

Solution :

→ Given :

• Last term , a(n) = 205

• Common difference , d = 6

• Number of terms , n = 34

→ To find :

• First term , a = ?

We know that ,

The nth term of an AP is given by ;

a(n) = a + (n - 1)d , where a is the first term and d is the common difference of the AP .

Now ,

Putting a(n) = 205 , d = 6 and n = 34 in the above formula , we get ;

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

=> 205 = a + (34 - 1)•6

=> 205 = a + 33•6

=> 205 = a + 198

=> a = 205 - 198

=> a = 7

Hence ,

First term , a = 7