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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:

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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

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