This is the question: The nth term of a sequence is given by Tn = 10n + 4. Put Tn < 100, and hence show that the nine terms T1 to T9 are less than 100. The answer is: < 9. Hence, there are 9 terms, 1 to 9 that are
less than 100.
But I don't understand, how do you know that from the answer of n, we can say 9 terms are less than 100? Please help me.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1

5

step-by-step explanation: