Question

if the first term of an ap is 31 and25th the term of an term us 140 more than the 5th term find the AP​

Answer 1

Answer:

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Step-by-step explanation:

=> 5th term = 31

=> a+(5-1)d=31

=> a+4d=31. .........1

=> 25th term = 140 + 5th term

=> a+(25-1)d=140+31

=> a+24d=171. .........2

=> equation 1- equation 2

=> a+4d - (a+24d) =31-171

=> a+4d-a-24d=-140

=> -20d=-140

=> d = -140/20

=> d = -7

=>d=7

=> Put d=7 in 1

=> a+4d=31

=> a+4×7=31

=> a+28=31

=> a=31-28

=> a=3

=> The given A. P. is

=> a,a+d,a+2d,a+3d,.......

=3,3+7,3+2×7,3+3×7,.........

=3,10,17,24,......

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Answer 2

Step-by-step explanation:

=> 5th term = 31

=> a+(5-1)d=31

=> a+4d=31. .........1

=> 25th term = 140 + 5th term

=> a+(25-1)d=140+31

=> a+24d=171. .........2

=> equation 1- equation 2

=> a+4d - (a+24d) =31-171

=> a+4d-a-24d=-140

=> -20d=-140

=> d = -140/20

=> d = -7

=>d=7

=> Put d=7 in 1

=> a+4d=31

=> a+4×7=31

=> a+28=31

=> a=31-28

=> a=3

=> The given A. P. is

=> a,a+d,a+2d,a+3d,.......

=3,3+7,3+2×7,3+3×7,.........

=3,10,17,24,......