Question

How many terms of a.p:34,32,30,......., must be taken to give a sum of 286?

Answer 1

Answer:

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Step-by-step explanation:

We have to find out n =?

Sn = (n / 2) ( a + l)

286 = (n / 2) (34 + 10)

572 = 44n

n = 572 / 44

n = 13

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Answer 2

Answer

No of terms = n = 13, 22

Explanation

AP ⇒ 34,32,30

∴ a = 34  

$d=a_{2} - a_{1}=32-34=-2$

$s_{n}=286$

To find

n= ??

Solution

We know that

$s_{n}=\frac{n}{2}[2a+(n-1)d]$

Putting given values we get

$s_{n}=\frac{n}{2}[2a+(n-1)d]$

$\longrightarrow 286 \:= \frac{n}{2}[2\times34+(n-1)-2]$

$\longrightarrow 286\times2=n[68-2n+2]$

$\longrightarrow 572 = n\times[70-2n]$

$\longrightarrow 572 =70n-2n^2$

$\longrightarrow 70n-2n^{2}-572=0\\\bf{Re \:Arranging\:terms\:we\:get$

$\longrightarrow2n^{2}-70n+572=0$

$\bf{Dividing \:Equation\:By\:2\:we\:get$

$\longrightarrow n^{2}-35n+286=0$

$\longrightarrow n^{2}-(22+13)n+286=0$

$\longrightarrow n^{2}-22n-13n+286=0$

$\longrightarrow n (n-22)-13(n-22)=0$

$\longrightarrow (n-22)(n-13)=0$

$\therefore\bf\underline{n=22\:OR\:13}$

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