Question

how many terms are there in the arthemetic series 1+3+5+....,+73+75

Answer 1

$\huge{ \underline{\bold {Given : }}}$

$\bold{AP \: is \: 1 + 3 + 5 + ... + 73 + 75}$

$Here \: a = 1$

$d = 3 − 1 = 2$

$\bold{nth \: term \: an = 75 nth \: term \: of \: AP \: is \: an}$

$\boxed{ \bold{= a + (n − 1)d }}$

$\: ⇒ 75 = 1 + (n − 1) × 2$

$\: ⇒ 74 = (n − 1) × 2$

$\: ⇒ 37 = (n − 1)$

$\: ∴ n = 38$

$\bold{Hence \: there \: are \: 38 \: terms \: in \: the \: given \: AP}$