Question

In an A.P. 8th term is 16 and 16th term is 48. (i) Find the common-difference of the A.P.​

Answer 1

Answer:

First term (a) = -12

Common difference (d) = 4

Step-by-step explanation:

Given => 8th term = 16

               16th term = 48

So ,

The general term of a A.P. is

a+(n - 1)d

So,

8th term can also be written as = a + 7d = 16

Similarly,

16th  term can also be written as = a + 15d = 48

Now ,

Subtracting both the equations we get,

a + 7d = 16

a + 15d = 48

-----------------

-8d = -32

8d = 32

d = 32/4

d = 4

Therefore,

a + 7d = 16

a = 16 - 7d

a = 16 - 7(4)

a = 16 - 28

a = -12

So the final answer is

First term (a) = -12

Common difference (d) = 4

Hope you understand.

Answer 2

SOLUTION

GIVEN

In an A.P. 8th term is 16 and 16th term is 48.

TO DETERMINE

The common-difference of the A.P.

EVALUATION

Let first term = a

Common Difference = d

8th term = 16

⇒ a + 7d = 16 - - - - - - (1)

16th term = 48

⇒ a + 15d = 48 - - - - - - (2)

Equation 2 - Equation 1 gives

8d = 32

⇒ d = 4

From Equation 1 we get

a = 16 - ( 7 × 4 ) = 16 - 28 = - 12

FINAL ANSWER

The common-difference of the A.P. = 4

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