Question

The value of 1 + 3 + 5 + 7 + 9 + ..........+25 is :
(A) 196
(B) 625
(C) 225
(D) 169​

Answer 1

$\huge{\mathcal{\blue{\underline{\underline{\pink{HeYa!!!}}}}}}$

${\large{\purple{\mathbb{ANSWER}}}}$

${\large{\blue{\bold{\underline{Given:-}}}}}$

▪︎ First term (a) = 1.

▪︎ Second term (a2) = 3.

▪︎ common difference (d) = 3-1 = 2.

▪︎ Last term (an) = 25.

${\large{\blue{\bold{\underline{To find:-}}}}}$

▪︎ Sum of n terms (sn) where nth term is 25.

${\large{\blue{\bold{\underline{Firstly,}}}}}$

▪︎ We have to find number of terms.

${\large{\blue{\bold{\underline{Formulas\:Used:-}}}}}$

▪︎ an = a+(n-1)d.

▪︎ Sn = n/2 (a+an)

${\large{\blue{\bold{\underline{Now,}}}}}$

=》 an = 25.

=》 a+(n-1)d = 25.

=》 1+(n-1)2 = 25.

=》 1+2n-2 = 25.

=》 -1+2n = 25.

=》 2n = 25+1.

=》 2n = 26.

=》 n = 26/2.

${\large{\red{\boxed{\bold{=》\:n\:=\:13.}}}}}$

▪︎ Therefore number of terms is 13.

${\large{\blue{\bold{\underline{So,}}}}}$

=》 S13 = 13/2 × (1+25)

= 13/2 (26)

= 13×26/2.

= 13 × 13.

${\large{\red{\boxed{\bold{=\:169.}}}}}$

Therefore option D is correct.

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