Question

check whether 137 is a term of A.P 3,11,19,27 .....?
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Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold\purple{137 \ is \ not \ the \ term \ of \ given \ A.P.}$

$\bold\orange{Given:}$

The given A.P. is 3,11,19,27,...

$\bold\pink{To \ find:}$

Whether 137 is a term of given A.P.

$\bold\purple{Explanation}$

We can check it by using formula

tn=a+(n-1)d

If we get 'n' as an integer the term will be of A.P.

$\bold\green{\underline{\underline{Solution}}}$

The given A.P. is 3,11,19,27,...

Here, a=3, d=11-3=8

Let tn be 137

By formula

tn=a+(n-1)d

137=3+(n-1)8

(n-1)8=137-3

(n-1)8=134

$\bold{n-1=\frac{134}{8}}$

But,134 is not perfectly divided by 8

(The answer goes in decimal

(But n is never in decimal)

Therefore,

$\bold\purple{137 \ is \ not \ the \ term \ of \ given \ A.P.}$

Answer 2

$\large{\underline{\bf{\pink{Answer:-}}}}$

✰⠀137 is not a term of given AP.

$\large{\underline{\bf{\blue{Explanation:-}}}}$

➼ In an AP with first term a and common difference d ,

the nth term is given by :-

an = a + (n - 1)d.

$\large{\underline{\bf{\green{Given:-}}}}$

✰ An AP is given as 3, 11 , 19, 27........etc.

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to check that 137 is a term of given AP or not.

$\huge{\underline{\bf{\red{Solution:-}}}}$

➼ First term (a) = 3

➼ Common difference (d) = 11-3

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=8

Let the nth term of AP be 137.

Then,

➼⠀an = 137

${\boxed{\bf{\purple{a_n=a+(n - 1)d}}}}$

➸⠀⠀⠀⠀⠀⠀137 = a+(n - 1)d

➸⠀⠀⠀⠀⠀⠀137 = 3 + (n - 1) 8

➸⠀⠀⠀⠀⠀⠀137 - 3 = (n - 1) 8

➸⠀⠀⠀⠀⠀⠀134 = (n - 1)8

➸⠀⠀⠀⠀⠀⠀134/8 = n - 1

➸⠀⠀⠀⠀⠀⠀(134/8 ) +1 = n

➸⠀⠀⠀⠀⠀⠀(134+8)/8 = n

➸⠀⠀⠀⠀⠀⠀142 /8 = n

So ,142 is not completely divided by 8 .

but , the number of terms cannot be a fraction.

Therefore, 137 is not a term of given AP.