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Grade: 11

                        

The sum of the series 1.3 2 +2.5 2 +3.7 2 +.... upto 20 terms. (A) 188090 (B) 180890 (C) 189820 (D) N.O.T

2 years ago

Answers : (1)

Arun
25211 Points
							
Given that 1.32, 2.52 3.72 .....................20 terms
Here 1,2,3,.................are in A.P.

a = 1, d = 1

tn = a + (n-1) d = 1 + (n -1)1 = n

3,5,7 ............. are in A.P
a = 3, d = 2
 
tn = a + (n-1) d = 3 + (n -1)2 = 2n + 1

∴ nth term = n(2n + 1)2 = 4n3 + 4n2 + n

Sum of n terms Sn = ∑ ( 4n+ 4n2 + n ) = 4 { n2(n+1)2}/4 + 4 {n (n+1)(2n+1)} / 6 + n(n+1)/2

                                                           = { n2(n+1)2} + 2 {n (n+1)(2n+1)} / 3 + n(n+1)/2
Sum of 20 terms S20 = 400×441 + 40 × 41 × 7 + 10 ×21 = 176400 + 11480 + 210 = 188090.
2 years ago
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