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# How many terms of the AP 26, 21 16, 11,

Question:

How many terms of the AP 26, 21 16, 11, …. are needed to give the sum 11?

Solution:

To Find: Number of terms required

Let the number of terms be n.

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

$\Rightarrow \frac{n}{2}[52+(n-1)(-5)]=11 \Rightarrow \mathrm{n}[52-5 n+5]=22$

$\Rightarrow n(57-5 n)=11 \times 2=11[57-5(11)]$

$\Rightarrow \mathrm{n}=11$

11 terms are required to give the sum 11 .