Question

If third term of an A.P. is four times of first term and sixth term is 17. find the series.

Answer 1

first term -- a
term3 = a + 2d, but term3 = 4a
4a = a+2d
3a = 2d

term6 = a + 5d = 17
or a = 17-5d

sub that into 3a = 2d
3(17-5d) = 2d
51 - 15d = 2d
51 = 17d
d = 3
then 3a = 6
a = 2

terms are: 2, 5, 8, 11, 14, 17 ,

all checks out,
the fourth terms is 4 times the first
and the 6th is 17

Answer 2

Actually you need to find series that means sum of the sequence..
That is formula of Sn=?
By using Tn=Sn-S(n-1)

Answer 3

Thanks to solve this question with explanation

Answer 4

Good

Answer 5

How to solve arithmetic progression