Question

the term of an Ap is 10,7,4.....is -64​

Answer 1

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

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$\green{\underline \bold{Given :}}$

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• -64 is a term of the given AP

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$\red{\underline \bold{To \: Find:}}$

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• Which term of this AP is -64

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\underline{\bold{\texttt{We know that,}}}$

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$\purple\longrightarrow$ $\sf a_n = a + (n - 1)d$

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• a = First term of the AP = 10

• n = Number of term = n

• d = Common difference = 7 - 10 = -3

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$\sf \longmapsto a_n = a + (n - 1)d$

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$\sf \longmapsto -64 = 10 + (n - 1)-3$

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$\sf \longmapsto -74 = -3n + 3$

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$\sf \longmapsto -77 = -3n +$

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$\sf \longmapsto 77 = 3n +$

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$\sf \longmapsto n = \dfrac { 77 } { 3 }$

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$\sf \longmapsto n = 25.66$

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As the value of n is not a natural number hence there is no term in this AP whose value is -64

$\rule{200}5$

Answer 2

Given:

10,7,4..........ii an Arithmetic Progression.

To Find:

Which term of this given A. P is -64.

Solution:

Let tn= -64

10,7,4.............. (Given)

Here, a=10 ,d=-3

tn=a+(n-1) d.......(Formula)

Now by substituting the values,

-64=10+(n-1) -3

-64=10-3n+3

-64-10=-3n+3

-74= -3n+3

3n=3+74

3n=77

n=77/3

Therefore,-64 is the 77/3 th term of an A. P