Question

which term of sequence 17,81/5,77/5,....is first negative term ?​

Answer 1

A.P sequence =

$17 \: \: \frac{81}{5} \: \: \frac{77}{5} ......$

a = 17

Common difference. =>

a2 - a1 = common difference.

a2 = 81/5.

A1 = 17.

$\frac{81}{5} - 17 = \frac{81 - 85}{5}$

$d = \frac{ - 4}{5}$

Now, we have to find out the first -ve term of the given series of AP.

So , after 0 the next place is of the 1st negative term ,so we will firstly find the place of 0

And we will got the place of 1st -ve term as the place next to 0 is the place of-ve term.

According to the formula:

an = a+ (n-1)d

0. = 17 + (n-1)-4/ 5

$0 = 17 - \frac{4n}{5} + \frac{4}{5}$

Now we will transfer 17 and 4/5 to LHS.

$\frac{ - 4}{5} - 17 = \frac{ - 4n}{5}$

$\frac{ - 4 - 85}{5} = \frac{ - 4n}{5}$

$- \frac{89}{5} = - \frac{4n}{5}$

$- \frac{89}{5} \times \frac{5}{4} = n$

$n = - \frac{89}{4}$

So , the place of 0 in the given series is

$- \frac{89}{4} = 22.25$

And place of 1st -ve term is next to 0.

So the place of 1st -ve term is 23

Hope it may help you

Answer 2

Step-by-step explanation:

A.P sequence =

17 \: \: \frac{81}{5} \: \: \frac{77}{5} ......17581577......

a = 17

Common difference. =>

a2 - a1 = common difference.

a2 = 81/5.

A1 = 17.

\frac{81}{5} - 17 = \frac{81 - 85}{5}581−17=581−85

d = \frac{ - 4}{5}d=5−4

Now, we have to find out the first -ve term of the given series of AP.

So , after 0 the next place is of the 1st negative term ,so we will firstly find the place of 0

And we will got the place of 1st -ve term as the place next to 0 is the place of-ve term.

According to the formula:

an = a+ (n-1)d

0. = 17 + (n-1)-4/ 5

0 = 17 - \frac{4n}{5} + \frac{4}{5}0=17−54n+54

Now we will transfer 17 and 4/5 to LHS.

\frac{ - 4}{5} - 17 = \frac{ - 4n}{5}5−4−17=5−4n

\frac{ - 4 - 85}{5} = \frac{ - 4n}{5}5−4−85=5−4n

- \frac{89}{5} = - \frac{4n}{5}−589=−54n

- \frac{89}{5} \times \frac{5}{4} = n−589×45=n

n = - \frac{89}{4}n=−489

So , the place of 0 in the given series is

- \frac{89}{4} = 22.25−489=22.25

And place of 1st -ve term is next to 0.

So the place of 1st -ve term is 23

Hope it may help you