Question

7th term of an HP is 3/2 and its 10th is 12/17. Find its first term and common difference

Answer 1

Hope this answer help you

Answer 2

Solution :-

Given that, 7th term = 3/2 and 10th term = 12/17

⇒ T₇ = 3/2 and T₁₀ = 12/17

⇒ 1/{a + (7 - 1)d} = 3/2 and 1/{a + (10 - 1)d} = 12/17

⇒ 1/(a + 6d) = 3/2 and 1/(a + 9d) = 12/17

⇒ 3a + 18d = 2 .................(1) and

⇒ 17a + 153d = 12 ................(2)

Multiplying the (1) by 17 and (2) by 3

(3a + 18d = 2)*17 

⇒ 51a + 306d = 34

(17a + 153d = 12)*3 

⇒ 51a + 459d = 36

Now. adding both we get.

51a + 306d = 34
51a + 459d = 36
_______________
          765d = 70
_______________

⇒ 765d = 70

d = 70/765

d = 14/153

Putting the value of d = 14/153 in (1).

3a + 18d = 2

3a + 18*14/153 = 2

3a = 252/153 = 2

3a = 2 - 252/153

3a = 306/153 - 252/153

3a = 54/153

a = 54/(153*3)

a = 18/153

a = 2/17

Answer.