a=-7 d=5 n=6 find an ARTHEMETIC PROGRESSIONS
Answers
Answer:
(1) 2, 4, 6, 8,....
The given sequence is an A.P.
Common difference = Second term − First term
= 4 − 2
= 2
(2) 2,
5
2
, 3,
7
3
,....
The given sequence is not an A.P.
(3) –10, –6, –2, 2...
The given sequence is an A.P.
Common difference = Second term − First term
= (−6) − (−10)
= 4
(4) 0.3, 0.33, 0.333,...
The given sequence is not an A.P.
(5) 0, –4, –8, –12,...
The given sequence is an A.P.
Common difference = Second term − First term
= (−4) − (0)
= −4
(6) -
1
5
,-
1
5
,-
1
5
,...
The given sequence is an A.P.
Common difference = Second term − First term
= (−
1
5
) − (−
1
5
)
= 0
(7) 3, 3+
√
2
, 3+2
√
2
, 3+3
√
2
The given sequence is an A.P.
Common difference = Second term − First term
= 3+
√
2
-3
=
√
2
(8) 127, 132, 137,...
The given sequence is an A.P.
Common difference = Second term − First term
= (132) − (127)
= 5
Answer:
We know that the formula for the nth term is t
n
=a+(n−1)d, where a is the first term, d is the common difference.
It is given that the first term is a=−7 and the difference is d=5, therefore,
t
12
=a+(n−1)d=−7+(12−1)5=−7+(11×5)=−7+55=48
Hence, t
12
=48