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NCERT Class XI Mathematics - Sequences and Series - Solutions

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Question : 5 of 106
Marks: +1, -0
ana_n = (1)n15n+1(-1)^{n-1} 5^{n+1}
Solution:  
We have, ana_n = (1)n15n+1(-1)^{n-1} 5^{n+1}
Substituting n = 1, 2, 3, 4, 5, we get
a1a_1 = (1)1151+1(-1)^{1-1} 5^{1+1} = (1)052(-1)^0 5^2 = 25 , a2a_2 = (1)2152+1(-1)^{2-1} 5^{2+1} = (1)153(-1)^1 5^3 = - 125
a3a_3 = ()3153+1(-)^{3-1} 5^{3+1} = (1)254(-1)^2 5^4 = 625, a4a_4 = (1)415+1(-1)^{4-1} 5^{+1} = (1)353(-1)^3 5^3 = - 3125
a5a_5 = (1)5155+1(-1)^{5-1} 5^{5+1} = (1)456(-1)^4 5^6 = 15625
∴ The first five terms are 25, – 125, 625, –3125, 15625.
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