Aljaneslabadanidn
Answered

IDNStudy.com, kung saan ang mga eksperto ay sumasagot sa iyong mga tanong. Makakuha ng mga sagot sa iyong mga tanong mula sa aming mga eksperto, handang magbigay ng mabilis at tiyak na solusyon.

Activity 7: summing Up

What is the sum of the terms of each finite sequence below?

1. 1, 4, 7, 10

2. 3, 5, 7, 9, 11

3. 10, 5, 0, -5, -10, -15

4. 81, 64, 47, 30, 13, -4

5.-2, -5, -8, -11, -14, -17

Sagot :

Indrawboyidn

The sum of the terms of each finite sequence

1. 22

2. 35

3. -15

4. 231

5. -57

Further explanation

Arithmetic sequence is an arrangement of numbers that has the same difference for consecutive pairs of numbers or it can be said that "the difference between one term and the next is a constant. (adding the same number to the next number) "

The arrangement of the numbers is like this:

[tex]\rm a,a+d,a+2d,a+3d,a+4d..etc[/tex]

a = initial term

d = different (common difference)

The formula for the nth term:

[tex]\rm \boxed{\bold{xn=a+d(n-1)}}[/tex]

While the formula for the sum of n terms:

[tex]\rm \boxed{\bold{\dfrac{1}{2}n(2a+(n-1)d}}[/tex]

From the problems above, it can be said that the series is an arithmetic sequence because they have the same difference

  • 1, 4, 7, 10

a = 1

d = 3

n = 4

[tex]\rm =\dfrac{1}{2}.4(2.1+(4-1)3)\\\\=2(2+9)\\\\=\boxed{\bold{22}}[/tex]

  • 3, 5, 7, 9, 11

a = 3

d = 2

n = 5

[tex]\rm =\dfrac{1}{2}.5(2.3+(5-1)2)\\\\=\boxed{\bold{35}}[/tex]

  • 10, 5, 0, -5, -10, -15

a = 10

d = -5

n = 6

[tex]\rm =\dfrac{1}{2}.6(2.10+(6-1).-5)\\\\=3(20-25)\\\\=\boxed{\bold{-15}}[/tex]

  • 81, 64, 47, 30, 13, -4

a = 81

d = -17

n = 6

[tex]\rm =\dfrac{1}{2}.6(2.81+(6-1).-17)\\\\=3(162-85)\\\\=\boxed{\bold{231}}[/tex]

  • -2, -5, -8, -11, -14, -17

a = -2

d = -3

n = 6

[tex]\rm =\dfrac{1}{2}.6(2.-2+(6-1).-3)\\\\=3(-4-15)\\\\=\boxed{\bold{-57}}[/tex]

Learn more

commoon difference of the sequence

https://brainly.ph/question/1721583

Insert two aritmetic means

https://brainly.ph/question/1543769

https://brainly.ph/question/1838784

#BetterWithBrainly

Pinahahalagahan namin ang bawat tanong at sagot na iyong ibinabahagi. Huwag kalimutang bumalik at magtanong ng mga bagong bagay. Sama-sama tayong magtatagumpay. Para sa mabilis at eksaktong mga solusyon, isipin ang IDNStudy.com. Salamat sa iyong pagbisita at sa muling pagkikita.