Question

Find the number of terms of an ap 18, 15*1/2,13...........,-49*1/2 and find the sum of all its terms

Answer 1

hope it helps you out

Answer 2

Answer:

$Sum \:of \: 28\: terms = -441$

Step-by-step explanation:

$Given \:A.P: 18,15\frac{1}{2},\\13,.....,-49\frac{1}{2}$

$First\:term(a)=18,\\common\: difference (d)=a_{2}-a_{1}\\=15\frac{1}{2}-18\\=-5\frac{1}{2}\\=-2.5\\Last\:term (a_{n})=-49.5$

$a+(n-1)d=-49.5$

$\implies 18+(n-1)(-2.5)=-49.5$

$\implies (n-1)(-2.5)=-49.5-18$

$\implies (n-1)(-2.5)=-67.5$

$\implies n-1=\frac{-67.5}{-2.5}$

$\implies n-1=27$

$\implies n = 27+1$

$\implies n = 28$

$Now,\\Sum \:of \:n\:terms(S_{n})=\frac{n}{2}[2a+(n-1)d]\\=\frac{28}{2}[2\times 18+(28-1)(-2.5)]\\=14[36+(27)(-2.5)]\\=14[36-67.5]\\=14\times (-31.5)\\=-441$

Therefore,

$Sum \:of \: 28\: terms = -441$

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