Question
If the sum of a certain number of terms of the A.P. 25,22,19, is 116 then the last term is
BITSAT
Mathematics
Sequences and Series
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. 0
- B. 2
- C. 4
- D. 6
Answer
C. 4
Step-by-step solution
a=25, d=22-25=-3 . Let n be the no. of terms array l Sum =116 ; \\ Sum = n 2 [2 a+(n-1) d] \\ 116= n 2 [50+(n-1)(-3)] \\ or 232=n[50-3 n+3]=n[53-3 n]=-3 n^ 2 +53 n \\ 3 n^ 2 -53+232=0 \\ (n-8)(3 n-29)=0 \\ n=8 or n= 29 3 , \\ n 29 3 \\ n=8 \\ Now, T _ 8 =a+(8-1) d=25+7 (-3)=25-21=4 \\ Last term =4 array
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