Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Here is a rule for generating a sequence; 3n+10 What is the 150th term of the sequence generate by this rule?​

Sagot :

MidnightShowers

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

Topic - Arithmetic Progression ( AP )

  • Given - a general term for a sequence.

  • To find - the 150th term of the given sequence

so let's start ~

General term , [tex] A_{n} [/tex] = 3n + 10

let's consider certain values of n to get some information with us which will help us solve the problem further !

let's first consider , n = 1 ! then ,

[tex]3n + 10 = 3(1) + 10 \\ \dashrightarrow \: 13[/tex]

now , let's consider n = 2

[tex]3n + 10 = 3(2) + 10 = 6 + 10 \\ \dashrightarrow \: 16[/tex]

then , let's consider n = 3

[tex]3n + 10 = 3(3) + 10 = 9 + 10 \\ \dashrightarrow \: 19[/tex]

hence ,

now we've with us an AP which is as follows -

[tex]13 \: , \: 16 \: , \: 19 \: ......[/tex]

from this Arithmetic Progression ,

we can know that

a = first term = 13

d = common difference = 16 - 13 = 19 - 16 = 3

now ,

[tex]A _{n} = a + (n - 1)d \\ \implies \: A _{150} = 13 + (149)(3) \\ \implies \: A _{150} = 13 + 447 \\ \pink{\implies \: A _{150} = 460}[/tex]

hope helpful :D

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.