Question bank/JEE Main/Mathematics

Let a_1, a_2,......... a_30, be an A.P., S =
$\sum_{i = 1}^{30}\mspace{2mu} a_{i}$ and
$T = \sum_{i = 1}^{15}\mspace{2mu} a_{(2i - 1)}$. If a_5 = -27 and
S-2T = 75, then a_10 is equal to

A47B42C52D57

Show answer and solution▾

S = a_1+ a_2 +.........+ a_30 =
T = a_1 + a_3 +.........+ a_29 =
and a_5 = 27 ⇒a+4d = 27
S-2T=75 ⇒ 15(2a+29d) -2(15(a+14d)) =75 ⇒ d= 5and a=7

Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx