Question

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

Answer 1

Answer:

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

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 , $A_{n}$ = 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 ,

$3n + 10 = 3(1) + 10 \\ \dashrightarrow \: 13$

now , let's consider n = 2

$3n + 10 = 3(2) + 10 = 6 + 10 \\ \dashrightarrow \: 16$

then , let's consider n = 3

$3n + 10 = 3(3) + 10 = 9 + 10 \\ \dashrightarrow \: 19$

hence ,

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

$13 \: , \: 16 \: , \: 19 \: ......$

from this Arithmetic Progression ,

we can know that

a = first term = 13

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

now ,

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

hope helpful :D