Question

find the AP if the 8th term of an ap is 31 and 15th is 6 more than the 11th term

Answer 1

t8=31
we know that,
tn=a+(n-1)d
t8=a+(8-1)d
t8=a+7d
31=a+7d...................(1)
BY THE 2ndGIVEN CONDITION
t15=t11+6
by using formula:tn=a+(n-1)d
a+14d=a+10d+6
14d=10d+6
14d-10d=6
4d=6
d=6/4
d=1.5
substitute d=1.5 in eqn (1)
31=a+7d
31=a+7(1.5)
31=a+10.5
31-10.5=a
a=20.5
NOW WE HAVE,
a=20.5 , d=1.5
t1=a=20.5
t2=a+d=20.5+1.5=22
t3=a+2d=20.5+2(1.5)=23.5
t4=a+3d=20.5+3(1.5)=25
so
IN this way we get an ARITHMETIC PROGRESSION
(AP)
20.5,22,23.5,25,......................
..HOPE.. THIS HELPS YOU
MY DEAR FRIEND TUSHAR