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ICSE Class 10 Answered

The sum of 5th and the 7th term of an A.P. is 4 and the 10th term is 46 . Find the A.P.
Asked by vrashbhan | 14 Jul, 2018, 02:16: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space straight a space be space the space first space term space and space straight d space be space the space common space difference.
Now comma
straight a subscript 5 space plus space straight a subscript 7 space equals space 4
rightwards double arrow straight a space plus space 4 straight d space plus straight a space plus space 6 straight d space equals space 4 space space..... since comma space straight a subscript straight n space equals space straight a space plus space left parenthesis straight n space minus 1 right parenthesis straight d
rightwards double arrow 2 straight a space plus space 10 straight d space equals space 4 space
rightwards double arrow straight a space plus space 5 straight d space equals space 2 space space space space...... left parenthesis 1 right parenthesis
Here comma space straight a subscript 10 space equals space 46
rightwards double arrow straight a space plus space 9 straight d space equals space 46 space space space.... left parenthesis 2 right parenthesis
Subtracting space left parenthesis 1 right parenthesis space from space left parenthesis 2 right parenthesis comma space we space get
rightwards double arrow 4 straight d space equals space 44
rightwards double arrow straight d space equals space 11
From space left parenthesis 1 right parenthesis comma space we space get
straight a space plus space 5 left parenthesis 11 right parenthesis space equals space 2 space
rightwards double arrow straight a space equals space 2 space minus space 55 equals negative 53
Therefore comma space the space required space straight A. straight P space is space straight a comma space straight a plus straight d comma space straight a space plus 2 straight d comma space straight a space plus 3 straight d comma.....
which space is space minus 53 comma space minus 42 comma space minus 31 comma space minus 20 comma...... end style
Answered by Yasmeen Khan | 16 Jul, 2018, 02:53: PM
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