The 8th term of an AP is 31 and its 15th term exceed its 11th term by 16 .find the AP and also its 20th term.
Answers
Answer:
20th term=79
AP:-3,7,11,15.....
Step-by-step explanation:
a is the 1st term in AP or GP
d is the common difference in AP
Therefore....the sum is.....
8th term (a+7d) = 31.........eqI
15th term (a+14d) - 11th term (a+10d) = 16
as 15th term is greater than 11th term of this AP by 16
the equation will be:-
(a+14d) - (a+10d)=16 .......eqII
a+14d-a-10d=16
positive 'a' and negative 'a' gets cancelled
14d-10d=16
4d=16
d=16/4
d=4
putting the value of 'd' from eqII in eqI....we get
a+7d=31
a+7*4=31
a+28=31
a=31-28
a=3
therefore first term 'a' = 3 ....and common difference 'd'= 4
the AP we get is:-
a,a+d,a+2d,a+3d......
3,7,11,15.....
and...20th term we get is
a+19d
3+(19*4)
3+76
79.....
you can check the abs by putting the value of 'a' and 'd' in the given 8th term's equation......thank uh
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Step-by-step explanation:
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