The number of terms common between the two series 2+5+8+..... upto 50 terms & the series 3+5+7+9+...... upto 60 terms is?

Asked by araima2001 | 10th Nov, 2015, 07:05: PM

Expert Answer:

C o n s i d e r space t h e space f i r s t space A. P. space 2 comma space 5 comma space 8 comma space 11 comma space 14 comma space 17 comma space 20 comma space 23 comma space... T h u s comma space f i r s t space t e r m space o f space t h e space A P space i s space 2 space a n d space c o m m o n space d i f f e r e n c e space i s space 3. H e n c e space 50 t h space t e r m space o f space t h e space A P space t subscript 50 equals a plus open parentheses n minus 1 close parentheses d equals 2 plus open parentheses 50 minus 1 close parentheses 3 equals 2 plus 147 equals 149  C o n s i d e r space t h e space s e c o n d space A. P. space 3 comma space 5 comma space 7 comma space 9 comma space 11 comma space 13 comma space 15 comma space 17 comma space 19 comma space 21 comma space 23... T h u s comma space f i r s t space t e r m space o f space t h e space A P space i s space 3 space a n d space c o m m o n space d i f f e r e n c e space i s space 2. H e n c e space 60 t h space t e r m space o f space t h e space A P space t subscript 60 equals a plus open parentheses n minus 1 close parentheses d equals 3 plus open parentheses 60 minus 1 close parentheses 2 equals 3 plus 118 equals 121  C o n s i d e r space t h e space c o m m o n space t e r m s space o f space t h e space a b o v e space t w o space A P apostrophe s colon 5 comma space 11 comma space 17 comma space 23 comma space 29 comma... T h u s comma space t h e space i n i t i a l space t e r m space o f space t h e space c o m m o n space A P equals 5 space a n d space c o m m o n space d i f f e r e n c e space o f space t h e space c o m m o n space A P equals 6 S i n c e space 121 space i s space t h e space l a s t space t e r m space o f space t h e space s e c o n d space A P comma space t h e space l a s t space t e r m space o f space t h e space c o m m o n space A P space w i l l b e space l e s s space t h a n space o r space e q u a l space t o space 121. C o n s i d e r i n g space t h e space l a s t space t e r m space o f space t h e space c o m m o n space A P space a s space 121 comma space w e space h a v e comma t subscript n equals a plus open parentheses n minus 1 close parentheses d rightwards double arrow 121 equals 5 plus open parentheses n minus 1 close parentheses 6 rightwards double arrow 121 minus 5 equals open parentheses n minus 1 close parentheses 6 rightwards double arrow 116 equals open parentheses n minus 1 close parentheses 6 rightwards double arrow open parentheses n minus 1 close parentheses equals 116 over 6 rightwards double arrow n minus 1 equals 19.3333.. rightwards double arrow n equals 19.3333.. plus 1 rightwards double arrow n equals 20.3333.. A s space apostrophe n apostrophe space c a n n o t space b e space f r a c t i o n comma space t a k i n g space t h e space n e a r e s t space w h o l e space n u m b e r comma space w e space h a v e comma space n equals 20 T h u s comma space t h e r e space a r e space 20 space c o m m o n space t e r m s space o f space t h e space t w o space g i v e n space A P s.

Answered by Vimala Ramamurthy | 11th Nov, 2015, 08:02: PM

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