Question

S10=4(s5) find ratio of first term to common difference

Answer 1

S10 = 4 ( S5 )

a ( first term )

d ( Common difference )


$sn = \frac{n}{2} (2a + (n - 1)d)$

$\frac{10}{2} (2a + 9d) = \frac{5}{2} (2a + 4d)$

10 ( 2a + 9d ) = 5 ( 2a + 4d )


$\frac{10}{5} (2a + 9d) = (2a + 4d)$

2 ( 2a + 9d ) = ( 2a + 4d )

4a + 18d = 2a + 4d

4a - 2a = 4d - 18d

2a = - 14 d


$a = \frac{ - 14d}{2}$

a = - 7d

$\frac{a}{d} = \frac{ - 7}{1}$

a : d = - 7 : 1