20th term from the end of the progression 20, 19 1/4, 18 1/2, 17 3/4, ......, -129 1/4 is _______.

Question

20^th term from the end of the progression \(20, 19\frac 14, 18\frac 12, 17 \frac 34,....,-129\frac 14 \) is ______.

(1) -120

(2) -115

(3) -125

(4) -110

Answer 1

Correct option is (2) -115

\(20, 19\frac 14, 18\frac 12, 17 \frac 34,....,-129\frac 14 \)

are in A.P. with common difference

\(d = 19\frac 14 - 20 = - \frac 34\)

20^th term from end = \(-129 \frac 14 + (20 - 1) (\frac 34)\)

\(= -129 \frac 14 +19. \frac 34\)

\(= \frac{-517}4 + \frac{57}4\)

\(= \frac{-460}4\)

\(= -115\)