Question

Find the sum of the first 25 terms of the ap 8,3,-2
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Answer 1

☞ GIVEN :-

(☬☬) A.P series is

8 , 3 , -2 , -------- , 25th term .

a (first term) = “ 8 ”

d(common difference) = (3 - 8) = -5

n (number of term's) = 25

☞ FORMULA :-

$\checkmark\:\tt{\bold\red{\boxed{S_n\:=\:{\dfrac{n}{2}}\:[2a\:+\:(n\:-\:1)\:d]\:}}}$

$\rm{\implies\:S_{25}\:=\:{\dfrac{25}{2}}\:[(2\times8)\:+\:(25\:-\:1)\times{(-5)}]\:}$

$\rm{\implies\:S_{25}\:=\:{\dfrac{25}{2}}\:[16\:-\:120]\:}$

$\rm{\implies\:S_{25}\:=\:{\dfrac{25}{2}}\:\times\:(-104)\:}$

$\rm{\implies\:S_{25}\:=\:-\:(25\times52)\:}$

$\rm{\implies\:S_{25}\:=\:-(1300)\:}$