Question

if fourth term of an hp is 3/5 and its 8 term is 1/3 then its first term is

Answer 1

H.P. is reciprocal of A.P.

so here I will vo with A.P.

a–» First term
d–»common difference.

4th term
$\frac{5}{3} \: and \: 8th \: term \: 3$

$a + 3d = \frac{5}{3} \: \: \: \: (1) \\ a + 7d = 3 \: \: \: (2) \\ subtracting \: eq \: (2) \: from \: (1) \\ \\ 4d = \frac{4}{3 } \\ d = \frac{1}{3} \\ putting \: value \: of \: d \: in \: eq.(1) \\ a + ( \frac{1}{3} ) \times 3 = \frac{5}{3} \\ a = \frac{5}{3} - 1 \\ a = \frac{2}{3}$

So, First term of A.P. is 2/3

$<b>$ Means first term of H.P. is 3/2

Answer 2

fourth term of hp is 3/5
eighth term of hp is 1/3
let the finalist 5/3 and 3/1 4th and 8th term of AP
t4=a+3d
5/3=a+3d (1)
t8=a+7d
3=a+7d. (2)
subtract 2 and 1
4d=4/3
d=1/3
substitute d in equation,
3=a+7×1/3
3-7/3=a
2/3 is first term is in AP.
hp is reciprocal of ap
hence 3/2 is first term of hp
hope you got it