Question

If 8th and 14th term of an HP are 1/2 and 1/3 respectively find 20th term

Answer 1

HP = 1 / AP. (opposite)


in AP

a+ 7d = 2 -----------> EQ. 1

a+ 13d = 3 ----------> EQ. 2

solve equation

then d= 1/6 , a = 5/6

then a + 19 d = ??

a + 19d = 5/6 + 19*(1/6)

= 5/6 + 19/6

= 24/6

= 4



then 20 th term = 4 (in AP)

and in HP = 1/4

Answer 2

Given 8th term of an HP = (1/2)

= > 1/(a + 7d) = (1/2)

= > a + 7d = 2 ------ (1)

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Given 14th term of an HP is 1/3.

= > 1/(a + 13d) = (1/3)

= > a + 13d = 3 ----- (2)

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On solving (1) & (2), we get

= > a + 7d = 2

= > a + 13d = 3

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-6d = -1

d = 1/6.

Substitute d = 1/6 in (1), we get

= > a + 7d = 2

= > a + 7(1/6) = 2

= > a + 7/6 = 2

= > a = 2 - 7/6

= > a = 5/6.

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Now,

20th term = 1/(a + 19d)

= > 1/(5/6 + 19(1/6))

= > (5/6 + 19/6)

= > 24/6

= > 4.

Therefore, 20th term of HP is 4.

Hope this helps!