Question

Check whether,-150 is a term of the A.P.11,8,5,2,.
....

Answer 1

No, –150 is not a term of A. P.

Thank you for question

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Answer 2

Step-by-step explanation:

AnswEr

Given AP is 11, 8, 5, 2 & so on.

• First term (a) = 11

• Common Difference (d), 8 - 11 = -3

Using nth term Formula of AP

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

$:\implies\tt -150 = 11 + (n - 1) (-3) \\\\\\:\implies\tt - 150 = 11 -3n + 3\\\\\\:\implies\tt - 150 - 14 = - 3n\\\\\\:\implies\tt - 164 = - 3n\\\\\\:\implies\tt n = \dfrac{\cancel{-} 164}{\cancel{ -} 3n}\\\\\\:\implies\boxed{\frak{\pink{ n = \dfrac{164}{3n}}}}$

Here, nth term of the AP is in fraction.

$\therefore$ Thus, -150 isn't a term of the AP.

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⠀$\boxed{\bf{\mid{\overline{\underline{\bigstar\: Formulaes \ related \ to \ AP \ : }}}}\mid}$⠀

$\begin{lgathered}\boxed{\begin{minipage}{15 em} \sf \displaystyle \bullet a_n=a + (n-1)d \\\\\\ \bullet S_n= \dfrac{n}{2} \left(a + a_n\right) \end{minipage}}\end{lgathered}$