Answer:
a = 14 and d = 6.67
Step-by-step explanation:
The nth term of an AP is given by :
[tex]a_n=a+(n-1)d[/tex]
Where
a is the first term and d is the common difference
ATQ,
An arithmetic sequence has the 7th term of 54 and the 13th term of 94 i.e.
[tex]a+6d=54\ ......(1)\\\\a+12d=94\ ........(2)[/tex]
Subtract equation (2) from (1).
a+6d-(a+12d) = 54-94
a+6d-a-12d = -40
-6d = -40
d = 6.67
Put the value of d in equation (1).
[tex]a+6(6.666)=54\\\\a=54-39.96\\\\a=14.04[/tex]
or
a = 14
Hence, the first term is 14 and the common difference is 6.67.
