Question

In the nth term of a progression is (4n-10)show that it is an ap
find first term,c.d,16th term​

Answer 1

ANSWER:

• The given expression is in A.P
• 16th term = 54

GIVEN:

• nth term of a progression is (4n-10)

TO FIND:

• 1st term and 16th term

SOLUTION:

nth term = 4n-10. ....(i)

Let us find the 1st , 2nd , 3rd term:

Putting n = 1 in eq(i)

1st term = 4(1)-10

= (-6)

Putting n = 2 in eq(i)

Second term = 4(2)-10

= 8-10

= (-2)

Putting n = 3 in eq(i)

Third term = 4(3) -10

= 12-10

= 2

Let us check whether the terms are in A.P or not

-6 , -2 , 2 ........

Common difference = (-2)-(-6)

= -2+6

= 4

Common difference = 2-(-2)

= 2+2

= 4

Yes they are in A.P

Formula

nth term = a+(n-1)d

where a = First term [Here a = (-6)]

d = Common difference [ Here d = 4]

n = number of terms ( here n = 16)

Putting values we get;

=> 16th term = -6+(16-1)4

=> 16 term = -6+60

=> 16th term = 54