Question

is 144 a term of the AP 3, 7, 11 ,... justify your answer​

Answer 1

Answer:

144is not term of given ap

Step-by-step explanation:

hope it will help you.

Answer 2

$\huge\underline\mathfrak{Question-}$

Is 144 a term of the AP 3, 7, 11..? Justify your answer.

$\huge\underline\mathfrak{Solution-}$

Given AP :

• 3, 7, 11..

We have to check whether 144 is a term of given AP or not.

Explanation :

Let 144 be the last term of given AP.

We know that,

$\large{\boxed{\rm{a_n(last\:term)=a+(n-1)d}}}$

$\begin{lgathered}\bold{Here} \begin{cases}\sf{a\:refers\:to\:the\:first\:term,\:that\:is\:3} \\ \sf{n\:refers\:to\:the\:number\:of\:terms}\\ \sf{d\:refers\:to\:the\:common\:difference,\:that\:is\:4}\end{cases}\end{lgathered}$

Now, putting the values,

$\longrightarrow$ 144 = 3 + ( n - 1 ) ( 4 )

$\longrightarrow$ 144 - 3 = 4n - 4

$\longrightarrow$ 141 + 4 = 4n

$\longrightarrow$ 145 = 4n

$\longrightarrow$ n = $\rm{\dfrac{145}{4}}$

$\longrightarrow$ n = 36.7

Here, the number of terms are in decimals, but they shouldn't be in decimals or fractions. So we can say that 144 is not any term of the given AP.

$\rule{200}1$