AP EAMCET201921 Apr 2019Morning ShiftMathematicsSequences and SeriesActual
If x= 3 10 + 3 7 10 15 + 3 7 9 10 15 20 + , then 5 x+8=
Options
- A5 5 3 3
- B5 5 3
- C3 3 5
- D25 5 3 3
Correct answer
D. 25 5 3 3
Step-by-step solution
Given, aligned & x= 3 10 + 3 7 10 15 + 3 7 9 10 15 20 + & x= 3 5 5 10 + 3 5 7 5 10 15 + 3 5 7 9 5 10 15 20 + & T_ r+1 = 3 5 7 (2 r+1) 5 r 1 2 3 r & = ( 2 5 )^r 3 / 2 5 / 2 7 2 (r+ 1 2 ) r ! & = (- 3 2 ) (- 3 2 -1 ) (- 3 2 -2 ) (- 3 2 -r+1 ) (- 2 5 )^r r ! aligned Comparing with general term of (1+x)^n, n R aligned & n(n-1)(n-2) (n-r+1) x^r r ! & = (- 3 2 ) (- 3 2 -1 ) (- 3 2 -r+1 ) (- 2 5 )^r r ! & n=- 3 2 , x=- 2 5 & x+ 8 5 = (1- 2 5 )^ -3 / 2 = ( 3 5 )^ -3 / 2 = ( 5 3 )^ 3 / 2 = 5 5 3 3 & 5 x+8 5 = 5 5 3 3 5 x+8=