1.

3. The general term of a sequence is given by a = - 4n+ 15. Is the sequence an A.P?Iso, find its 15th term and the common difference.

Answer»

an = - 4n + 15 also 15 - 4nan = a + ( n - 1 ) da1 = 15 - 4 × 1 = 15 - 4 = 11 a2 = 15 - 4 × 2 = 15 - 8 = 7 a3 = 15 - 4 × 3 = 15 - 12 = 3

AP : 11 , 7 , 3

sn = n/2 { 2a + (n-1) d } sn = 3 / 2 { 2 × 11 + (3-1) -4 sn = 3 /2 { 22 + 2 × - 4 } sn = 3/2 { 22 + (-8) }sn = 3/2 { 22 - 8 }sn = 3/2 × 14 sn = 3 × 7 sn = 21

Hence Sn = 21



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