Question

determin the A. P. whose t3 =5 and t7 = 9
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Answer 1

Answer:

3rd term of the AP: a+2d = 5 …(1)

7th term: a+6d = 9 …(2)

Subtract (1) from (2)

4d = 4, or

d = 1 and so a = 3.

The AP is 3,4,5,6,….

Answer 2

Answer :

The A.P. is  3 , 4 , 5 , 6 , ....

Step-by-step explanation :

Given,

• third term, t₃ = 5
• seventh term, t₇ = 9

To find,

• the A.P.

Solution,

 nth term of an A.P. is given by,

   tₙ = a + (n - 1)d

where

  a is the first term

  d is the common difference

Third term = 5

t₃ = a + (3 - 1)d

5 = a + 2d ---[1]

Seventh term = 9

t₇ = a + (7 - 1)d

9 = a + 6d ---[2]

equation [2] - equation [1]

 a + 6d - (a + 2d) = 9 - 5

 a + 6d - a - 2d = 4

      4d = 4

        d = 4/4

        d = 1

Common difference, d = 1

Substitute d = 1 in equation [1],

 5 = a + 2d

 5 = a + 2(1)

 5 = a + 2

 a = 5 - 2

 a = 3

First term, a = 3

Second term,

t₂ = a + (2 - 1)d

t₂ = 3 + 1(1)

t₂ = 3 + 1

t₂ = 4

$\dag$ The required A.P. is 3 , 4 , 5 , 6 ....