If sixth term of a H-P- is 1-61 and its tenth term is 1-105- then first term of that H-P- is

The correct option is C T_6 of H.P. = 1/61⇒ T_6 of A.P. = 61 and T_10 of H.P. = 1/105⇒ T_10 of A.P. = 105, so, a + 5d = 61 ........(i) and a + 9d = 105 nbs ...

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Standard IX

Mathematics

Harmonic Progression

If sixth term...

Question

If sixth term of a H.P. is $\frac{1}{61}$ and its tenth term is $\frac{1}{105}$ , then first term of that H.P. is

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Solution

The correct option is C

$T_{6}$ of H.P. = $\frac{1}{61} \Rightarrow T_{6}$ of A.P. = 61

and $T_{10}$ of H.P. = $\frac{1}{105} \Rightarrow T_{10}$ of A.P. = 105,

so, a + 5d = 61 ........(i) and a + 9d = 105 .....(ii)

From (i) and (ii), a= 6

Therefore first term of H.P. = $\frac{1}{a}$ = $\frac{1}{6}$ .

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If sixth term of a H.P. is 161 and its tenth term is 1105, then first term of that H.P. is

The correct option is C T6 of H.P. = 161⇒T6 of A.P. = 61 and T10 of H.P. = 1105⇒T10 of A.P. = 105, so, a + 5d = 61 ........(i) and a + 9d = 105 .....(ii) From (i) and (ii), a= 6 Therefore first term of H.P. = 1a = 16.

If sixth term of a H.P. is $\frac{1}{61}$ and its tenth term is $\frac{1}{105}$ , then first term of that H.P. is