Question
Statement-I : 1, 2, 4, 8, ......... is a G.P., 4, 8, 16, 32 is a G.P. and 1 + 4, 2 + 8, 4 + 16, 8 + 32, ....... is also a G.P.
Statement-II : Let general term of a G.P. (with positive terms) with common ratio r be Tk + 1 and general term of another G.P. (with positive terms) with common ratio r be T'k + 1, then the series whose general term T''k + 1 = Tk + 1 + T'k + 1 is also a G.P. with common ratio r.
- Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
- Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I.
- Statement-I is true, Statement-II is false.
- Statement-I is false, Statement-II is true.
Hint:
find out the terms of the 3rd sequence in statement and check whether it satisfies the statement
The correct answer is: Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I.
Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
in statement 1:
1,2,4 8 is a GP with r = 2
4,8,16,32 is a GP with r =2
5, 10, 20, 40,80… is a GP with r = 2
Hence, the statement 2 is a correct explanation of statement 1
the mathematical reasoning can be proved by observing the term of the sequences
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