Question

What is the sum of the geometric sequence 3, 15, 75, … if there are 7 terms
39,062
58,593
195,312
292,968

Answer 1

at first, what is the common ratio, and the first term?

Answer 2

The formula for the sum is, \(\Large\color{black}{ \displaystyle {\rm \LARGE S}_{n}=\frac{a_1\left(1-r^{n}\right)}{1-r}}\)

Answer 3

where 'n' is number of terms, \(\Large\color{black}{a_1}\) is the first term, and 'r' is the common ratio.

Answer 4

I know how to deduce it though

Answer 5

algebraically, without this formula

Answer 6

no, you do he formula, and I will post my thingy

Answer 7

ok

Answer 8

from 3 we are multiplying times 3, so
`(2nd term)+(3rd term)` => will form sum number divisible by 10.
`(4th term)+(5th term)` => will form sum number divisible by 10.
`(6th term)+(7th term)` => will form sum number divisible by 10.

like
15 + 75 = 90 (has 0 at the end)
and so will the other 2 sums be, `4th+5th` AND `6th+7th` have 0 at the end.

and therefore, the sum of all 6 last terms (not including the first) will get you a number that is divisible by 10.


And if so, then after you add 3 to this number, `_ _ _ , _ _0 ` + 3 = `_ _ _ , _ _3 `

THE LAST DIGIT IN THE ANSWER IS 3.

Answer 9

I got 58,593

Answer 10

good

Answer 11

my first line has a typo

Answer 12

from 3 we are multiplying times 5, so
(times 5, not times 3)

Answer 13

I will depart for a small chess game for now.... excuse that