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