Question

find the 10th term of

1/4
-1/2
1
-2
4

Answer 1

Hi , friend!!

d = a2 - a1

so d = -1/2 - 1/4

d = -3/4


now , 10th term


=> a + (n -1) × d


1/ 4 + ( 9 × -3/4 )

1/4 + ( -27 / 4 )


=> -26 / 4

-13 / 2

hope it help !!

thanks

Answer 2

In the given progression, we have

$( \frac{ - 1 }{2} ) \div \frac{1}{4} = \frac{ - 1}{2} \times 4 = - 2 \\ \\ 1 \div \frac{ - 1}{2} = 1 \times( - 2) = - 2 \\ \\ - 2 \div 1 = - 2 \\ \\ 4 \div ( - 2) = 4 \times ( \frac{ - 1}{2} ) = - 2 \\ \\ \\ So, \: the \: given \: progression \: is \: GP. \\ \\ where, \: a = \frac{ 1}{4} \: \: \: \: \: \: and \: \: \: d = - 2 \\ \\ {10}^{th} \: term \: of \: GP \: = a \times {r}^{(10 -1 )} \\ \\ = \frac{1}{4} \times { - 2}^{9} \\ \\ = \frac{ - 512}{4} \\ \\ = - 128$

So , 10 term of the given GP is -128.