If (21)18 + 20·(21)17 + (20)2 · (21)16 + ……….. (20)18 = k (2119 – 2019) then k =
If (21)18 + 20·(21)17 + (20)2 · (21)16 + ……….. (20)18 = k (2119 – 2019) then k =
\(\frac{21}{20}\)
1
\(\frac{20}{21}\)
0
The Correct Option is B
Solution and Explanation
The correct answer is option (B): 1
\(a=(21)^{18}.r=\frac{20}{21},n=19\)
\(S=(21)^{18}=\frac{(1-(\frac{20}{21})^{19})}{1-\frac{20}{21}}\)
\(\Rightarrow \frac{(21)^{19}}{(21)^{19}}(21^{19}-20^{19})\)
\(\Rightarrow(21^{19}-20^{19})=1\)
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Concepts Used:
Arithmetic Progression
Arithmetic Progression (AP) is a mathematical series in which the difference between any two subsequent numbers is a fixed value.
For example, the natural number sequence 1, 2, 3, 4, 5, 6,... is an AP because the difference between two consecutive terms (say 1 and 2) is equal to one (2 -1). Even when dealing with odd and even numbers, the common difference between two consecutive words will be equal to 2.
In simpler words, an arithmetic progression is a collection of integers where each term is resulted by adding a fixed number to the preceding term apart from the first term.
For eg:- 4,6,8,10,12,14,16
We can notice Arithmetic Progression in our day-to-day lives too, for eg:- the number of days in a week, stacking chairs, etc.
Read More: Sum of First N Terms of an AP