Question

Write the related series for the finite sequence 7.6, 6.3, 5, ... , –1.5. Then evaluate the

series.

7.6 + 6.3 + 5 + ... + (–1.5) = 17.4

7.6 + 6.3 + 5 + (–1.5) = 17.4

7.6 + 6.3 + 5 + ... + (–1.5) = 24.4

none of these

Answer 1

@Michele_Laino

Answer 2

@tkhunny

Answer 3

it is an arithmetic series, whose constant is:
\[\huge d = 7.6 - 6.3 = 6.3 - 5 = ...?\]

Answer 4

what does that mean?

Answer 5

what is \(d\) ?

Answer 6

so would you find the value of 7.6- 6.3 amd 6.3-5

Answer 7

it is 1.3

Answer 8

yes! More precisely it is \(d=-1.3\)

Answer 9

now, the last term is: \(-1.5\), so we can write:
\[\huge - 1.5 = 7.6 + \left( {n - 1} \right) \cdot \left( { - 1.3} \right)\]
where \(n\) is the number of terms of the sequence. Please solve for \(n\)

Answer 10

how would i solve for N?

Answer 11

here is my hint:
we can write this:
\[\huge n - 1 = \frac{{ - 1.5 - 7.6}}{{ - 1.3}} = ...?\]
please continue

Answer 12

-7

Answer 13

I got \(n-1=7\)

Answer 14

o yeah sorry two negatives make a positive

Answer 15

so n=8

Answer 16

that's right!
the number of terms of the sequence is:
\[\huge n =8\]

Answer 17

now, the sum of all terms of the sequence is given by the subsequent formula:
\[\large {S_8} = \frac{{{a_1} + {a_8}}}{2} \times 8 = \frac{{7.6 + \left( { - 1.5} \right)}}{2} \times 8 = ...?\]

Answer 18

i got 24.4

Answer 19

that's right!

Answer 20

so c

Answer 21

yes!

Answer 22

Thank you so much for your help

Answer 23

:)