The first term of two A.P.s are equal and the ratios of their common differences is 1:2 If the 7th term of first A.P and 21th term of second A.P are 23 and 125 respectively. Find two A.P.s

Asked by www.maniyarsufiyan13 | 26th Jun, 2020, 12:19: AM

Expert Answer:

Let the first term be a
Common differences of the first and second APs be d1 and d2 respectively.
7th term = 23 and 21st term = 125
rightwards double arrow straight a plus 6 straight d subscript 1 equals 23 space space rightwards double arrow space straight a space equals space 23 minus 6 straight d subscript 1 space space... space left parenthesis straight i right parenthesis space and
straight a plus thin space 20 straight d subscript 2 equals 125 space rightwards double arrow space straight a space equals space 125 minus 20 straight d subscript 2 space... space left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space get
23 minus 6 straight d subscript 1 equals 125 minus 20 straight d subscript 2 space
20 straight d subscript 2 minus 6 straight d subscript 1 equals 102
10 straight d subscript 2 minus 3 straight d subscript 1 equals 51 space space... space left parenthesis iii right parenthesis
But space straight d subscript 1 colon straight d subscript 2 space equals space 1 colon 2
rightwards double arrow straight d subscript 2 equals 2 straight d subscript 1
From space left parenthesis iii right parenthesis
20 straight d subscript 1 minus 3 straight d subscript 1 equals 51
17 straight d subscript 1 equals 51
straight d subscript 1 equals 3
straight d subscript 2 equals 6
rightwards double arrow straight a plus 18 equals 23 rightwards double arrow straight a equals 5 space space... space From space left parenthesis straight i right parenthesis
Hence comma space the space two space APs space are space 5 comma space 8 comma space 11 comma space 14 comma space.... space space space and space space 5 comma space 11 comma space 17 comma space 23 comma space...

Answered by Renu Varma | 28th Jun, 2020, 05:03: PM