CAN I GET HELP WITH THIS QUESTION ABOUT SEQUENCE AND SERIES plsss!!! in screenshot

Question

CAN I GET HELP WITH THIS QUESTION ABOUT SEQUENCE AND SERIES   plsss!!! in screenshot

hari5719 · Answer

attachment

hari5719 · Answer

i really dont know !!

anonymous · Answer

@imqwerty

hari5719 · Answer

@ikram002p

owlcoffee · Answer

Okay, first of all, we might want to find the ratio of proportionality, this being:$$\frac{ u_9 }{ u_4 }=35$$
From here you can see that we can calculate u9 and that the ratio is indeed 35:
$$u_9=(35)(135)$$
Now, here we might want to use, the formula of a geometric series:
$$u_n=(u_1)(r ^{n-1})$$
Where Un is any term you like and U1 is the one you want to calculate:
$$u_4=(u_1)(r^3)$$
then
$$135=(u_1)(35^3)$$

hari5719 · Answer

then?

owlcoffee · Answer

Solve for u1 there.

hari5719 · Answer

oh  i dont understand the second sub division ?

owlcoffee · Answer

What do you mean?

hari5719 · Answer

@Owlcoffee  ike how do i do  $$S10 =a(b-1)$$

anonymous · Answer

srry @Owlcoffee  i think ratio is 3^5

owlcoffee · Answer

Ah, okay the process is analogous just change 35 for 3^5

owlcoffee · Answer

now a sum of terms of a geometric series is defined as:
$$S_n=\frac{ a_1(1-r^n) }{ 1-r }$$
so, S10 will be:
$$S _{10}=\frac{ (1-r ^{10}) }{ 1-r }$$
Replace that with the ratio "r" and that has to be equal to a(b-1)

hari5719 · Answer

Thank you GUYS @Owlcoffee  @ayeshaafzal221