First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an

S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d] → Equation (1)

S=an+an−1+an−2+an−3+...+a1

S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d] → Equation (2)

Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)

2S=n(a1+an)
S=n/2(a1+an)

Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]

5 0

3 years ago

PLEASE ANSWER THIS ONE!!!

Oliga [24]

Answer:

6:5

Step-by-step explanation:

i think this is it as I square rooted it and go that

7 0

3 years ago

Jake has five cats and then he finds ten more cats how many does jake have after he loses 11 cats

AleksandrR [38]

jake has 5 cats

then he finds 10 cats

jake now has 5+10 = 15 cats

now he loses 11 cats

15 -11 =4

jake now has 4 cats

8 0

4 years ago

Read 2 more answers

In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20

DiKsa [7]

The percentage of winning if 20 winning numbers are randomly selected from numbers 1 to 80 is 12.48%.

Given There are 80 numbers from which 20 numbers are selected randomly in a game of Keno by player and after selection of 20 winning numbers again 20 numbers are selected and player wins if the player has correctly selected 3,4,or 5 of the 20 winning numbers.

Probability is the chance of happening an event among all the events possible.

Probability of winning is calculated as under:

Probability= $C(20,3)C(60,17)/C(80,20)$

We have taken C(20,3) because player will win if 5 numbers are selected from 20 winning numbers.

We have taken C(60,17) because after selection of 20 numbers 60 numbers will left from 80 and after winning from 3 numbers 17 numbers left and from total 80, 20 numbers are taken.

=C(20,3)C(60,17)/C(80,20)

=(20!/3!17! * 60!/17!43!)/80!/20!60!

=1140*387221678682300/35353161422121743200

=12.48%

Hence the probability of winning is 12.48%.

Learn more about probability at brainly.com/question/24756209

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5 0

2 years ago