Answered

IDNLearn.com provides a collaborative platform for sharing and gaining knowledge. Find accurate and detailed answers to your questions from our experienced and dedicated community members.

The third term in an arithmetic sequence is 14 and the fifth term is 20. If the first term is a1, which is an equation for the nth term of this sequence?

Sagot :

Akabane009idn

Answer:

The equation for nth term is 3n + 5.

Step-by-step explanation:

Let a1 be a,

a3 = a + (n - 1)d

or, 14 = a + (3 - 1)d

so, 14 = a + 2d

Now,

a5 = a + (n - 1)d

or, 20 = a + (5 - 1)d

or, 20 = a + 4d

now,

a + 4d = 20

a + 2d = 14

now,

a + 4d - ( a + 2d) = 20 - 14

or, a + 4d - a - 2d = 6

or, 2d = 6

so, d = 3

Now,

a + 2d = 14

or, a + 2(3) = 14

or, a = 14 - 6

so, a = 8

Now,

an = a + (n - 1)d

or, an = 8 + (n - 1)3

or, an = 8 + 3n - 3

so, an = 3n + 5

Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.