what is the sum of the first 14 terms of an arithmetic sequence if the 5th term is 31 and the 9th term is 59?​

Answers

Answer 1
Given:

5th term of an AP = 31

9th term = 59

Find:

the sum of the first 14 terms of an arithmetic sequence

Solution:

We know that,

nth term of an AP – a(n) = a + (n - 1)d

Hence,

⟹ a + (5 - 1)d = 31

⟹ a + 4d = 31 -- equation (1)

Similarly,

⟹ a + (9 - 1)d = 59

⟹ a + 8d = 59 -- equation (2)

Subtract equation (1) from (2).

⟹ a + 8d - ( a + 4d ) = 59 - 31

⟹ a + 8d - a - 4d = 28

⟹ 4d = 28

⟹ d = 28/4

⟹ d = 7

Substitute the value of d in equation (1).

⟹ a + 4(7) = 31

⟹ a + 28 = 31

⟹ a = 31 - 28

⟹ a = 3

Now,

Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]

⟹ S(14) = 14/2 * [ 2(3) + (14 - 1)(7) ]

⟹ S(14) = 7 [ 6 + 91 ]

⟹ S(14) = 7 * 97

⟹ S(14) = 679

∴ The sum of first 14 terms of the given AP is 679.

I hope it will help you.

Regards.


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Step-by-step explanation:

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Step-by-step explanation:

When we subtract a negative number, it's basically a double negative, kind of like how we don't use those in English. We want to turn that into a positive, and double negatives are positive.

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Step-by-step explanation:

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Answers

Answer: 1) D    2) B, A     3) A

Step-by-step explanation:

Domain is the x-values

Range is the y-values

Graph is a function if no x-values are duplicated

1) option D

  (3, 7), (1, 0), (8, 1), (-4, -3), (2, 7)

   ↓       ↓       ↓        ↓          ↓

Domain: x = {1, 1, 8, -4, 2}   → No duplicates so it is a function.

  (3, 7), (1, 0), (8, 1), (-4, -3), (2, 7)

       ↓       ↓       ↓          ↓        ↓

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y-values are between -5 (included = bracket) and +5 (included = bracket)

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Answers

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Step-by-step explanation:

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Answer:

y= -2x-2

Step-by-step explanation:

All parallel lines have the same slope. So, the line we create must have a slope of -2. If we multiply the x value by -2, we can find b through an equation.

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So, our equation would be

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Step-by-step explanation:

Tangela earns the same amount each week by babysitting. When she started this job, she had $200 in her savings account. The table shows Tangela's savings account balance for her first month of work. Week 0 1 2 3 4 Balance $200 $350 $500 $650 $800 Let x represent the number of weeks Tangela has been working and let y represent Tangela's account balance. Which equation, expressed in Slope-Intercept form, represents the amount of money in Tangela's bank account over time?

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Answers

Answer:

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Step-by-step explanation:

Given that:

Week : ____ 0___ 1 ___ 2 ____3 _____4

Balance : __200_350 _ 500 _ 650 ___800

Amount had in savings account = $200 before starting the job

x = number of weeks spent working

y = account balance

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