the sum of first m terms of  an A.P. is 4m^2-m. If its nth term is 107 find the value of n. Also find the 21st term of this A.P.?

Asked by Shivam Goyal | 9th Dec, 2014, 10:03: PM

Expert Answer:

G i v e n space t h a t space s u m space o f space f i r s t space m space t e r m s space o f space a n space A. P equals 4 m squared minus m W h e n space m equals 1 comma space w e space h a v e comma space S subscript 1 equals 4 cross times 1 squared minus 1 equals 3 B u t space S subscript 1 equals a rightwards double arrow a equals 3 W h e n space m equals 2 comma space w e space h a v e comma space S subscript 2 equals 4 cross times 2 squared minus 2 equals 16 minus 2 equals 14 B u t space S subscript 2 equals a subscript 1 plus a subscript 2 equals a plus a plus d equals 14 rightwards double arrow 2 a plus d equals 14 rightwards double arrow 2 cross times 3 plus d equals 14 rightwards double arrow 6 plus d equals 14 rightwards double arrow d equals 14 minus 6 rightwards double arrow d equals 8 G i v e n space t h a t space a subscript n equals 107 rightwards double arrow a plus open parentheses n minus 1 close parentheses cross times d equals 107 rightwards double arrow 3 plus open parentheses n minus 1 close parentheses cross times 8 equals 107 rightwards double arrow open parentheses n minus 1 close parentheses cross times 8 equals 107 minus 3 rightwards double arrow open parentheses n minus 1 close parentheses cross times 8 equals 104 rightwards double arrow open parentheses n minus 1 close parentheses equals 104 over 8 rightwards double arrow open parentheses n minus 1 close parentheses equals 13 rightwards double arrow n equals 13 plus 1 rightwards double arrow n equals 14 W e space n e e d space t o space f i n d space a subscript 21 : a subscript 21 equals 3 plus open parentheses 21 minus 1 close parentheses cross times 8 rightwards double arrow a subscript 21 equals 3 plus 20 cross times 8 rightwards double arrow a subscript 21 equals 3 plus 160 rightwards double arrow a subscript 21 equals 163

Answered by Vimala Ramamurthy | 10th Dec, 2014, 10:36: AM

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