jessicathegr823
29.06.2019 •
Mathematics
Need answered asap will reward brainliest pick method (1) or (2) to find the partial sum of the first 100 terms for this sequence. 1. use the explicit formula, an = a1 + (n-1) d to find the 100th term for this sequence. then use the partial sum formula sn = n/2 (a1 + an) formula to find s100. 2. use technology () to find s100 using sigma notation with the explicit formula. ∑100n=1(a1 +(n−1)d) explain which method you used, show or explain what you did and remember to give your answer too.
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Ответ:
The sum of the first 100 terms is 60400
Step-by-step explanation:
* Lets revise the arithmetic sequence
- There is a constant difference between each two consecutive
numbers
- Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic sequence:
- U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
- Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms n is the position of the
number
- The sum of first n terms of an Arithmetic sequence is calculate from
Sn = n/2[a + l], where a is the first term and l is the last term
* Now lets solve the problem
- We will use method (1)
- From the table the terms of the sequence are:
10 , 22 , 34 , 46 , 58 , 82 , 94 , , where 10 is the first term
∵ an = a1 + (n - 1) d ⇒ explicit formula
∵ a1 = 10 and a2 = 22
∵ d = a2 - a1
∴ d = 22 - 10 = 12
- The 100th term means the term of n = 100
∴ a100 = 10 + (100 - 1) 12
∴ a100 = 10 + 99 × 12 = 10 + 1188 = 1198
∴ The 100th term is 1198
- Lets find the sum of the first 100 terms of the sequence
∵ Sn = n/2[a1 + an]
∵ n = 100 , a = 10 , a100 = 1198
∴ S100 = 100/2[10 + 1198] = 50[1208] = 60400
* The sum of the first 100 terms is 60400
Ответ:
We have this given information:
-one half of the bag is peanuts.
-1/4 is chocolate candies
-1/4 is dried fruit
We know one-quarter of the bag is chocolate candies. So, if you were to draw a chocolate candy:
1/2+1/4+1/4= 1
1/4=.25 <== Convert that into percentage.
You have a 25% chance of drawing a chocolate candy.
I hope this helps!
~kaikers