Question

help! hurry!! NO SPAM!!!! I will mark brainliest if you get it correct and show your work.Identify the 15th term of the arithmetic sequence in which a5 = 10 and a10 = 20.

Answer 1

Answer:

a₁₅ = 30

Step-by-step explanation:

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ = 10 and a₁₀ = 20 , then

a₁ + 4d = 10 → (1)

a₁ + 9d = 20 → (2)

Subtract (1) from (2) term by term to eliminate a₁

5d = 10 ( divide both sides by 5 )

d = 2

Substitute d = 2 into (1) and solve for a₁

a₁ + 4(2) = 10

a₁ + 8 = 10 ( subtract 8 from both sides )

a₁ = 2

Then

a₁₅ = 2 + (14 × 2) = 2 + 28 = 30

Answer 2

Answer:

  30

Step-by-step explanation:

Evenly-spaced terms of an arithmetic sequence are an arithmetic sequence. You are given terms 5 and 10 and asked to find term 15. The difference between term 15 and term 10 will be the same as the difference between term 10 and term 5.

  5d = a10 -a5 = 20 -10 = 10 . . . . . . . this is 5 times the common difference (d)

  a15 = a10 +5d = 20 +10 = 30

The 15th term is 30.

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Additional comment

Another way to look at this is that a10 is the midpoint between a15 and a5. That means ...

  a10 = (a15 +a5)/2

  a15 = 2(a10) -a5 = 2(20) -10 = 30