Question
if 8th term of an AP is equal to 5 terms its second term .if the 5th term is 8 find the first 10 terms
Answers
Reiny
term8 = a+7d
term2 = a+d
a+7d = 5(a+d)
a + 7d = 5a + 5d
2d = 4a
d = 2a
term5 = a+4d = 8
a + 4(2a) = 8
9a = 8
a = 8/9 ---> d = 16/9
terms are:
8/9, 24/9, 40/9, 56/9, 72/9, 88,9, 104/9, 120/9, ...
carry on
check:
5 times the 2nd
= 5(24/9) = 120/9 which is term 8
term2 = a+d
a+7d = 5(a+d)
a + 7d = 5a + 5d
2d = 4a
d = 2a
term5 = a+4d = 8
a + 4(2a) = 8
9a = 8
a = 8/9 ---> d = 16/9
terms are:
8/9, 24/9, 40/9, 56/9, 72/9, 88,9, 104/9, 120/9, ...
carry on
check:
5 times the 2nd
= 5(24/9) = 120/9 which is term 8