Question -
Answer -
(i) 7, 13, 19, тАж,205
Solutions:
(i) Given, 7, 13,19, тАж, 205 is the A.P
Therefore
First term, a┬а= 7
Common difference, d┬а=┬аa2┬атИТ┬аa1┬а=13 тИТ 7 = 6
Let there are┬аn┬аterms in thisA.P.
an┬а= 205
As we know, for an A.P.,
an┬а=┬аa┬а+ (n┬атИТ 1)┬аd
Therefore, 205 = 7 + (n┬атИТ 1) 6
198 = (n┬атИТ 1) 6
33 = (n┬атИТ 1)
n┬а= 34
Therefore, this given series has 34 terms init.
First term, a┬а= 18
Common difference, d = a2-a1┬а=
d = (31-36)/2 = -5/2
Let there are n terms in this A.P.
an┬а= 205
As we know, for an A.P.,
an┬а=┬аa+(nтИТ1)d
-47 = 18+(n-1)(-5/2)
-47-18 = (n-1)(-5/2)
-65 = (n-1)(-5/2)
(n-1) = -130/-5
(n-1) =┬а26
n┬а= 27
Therefore, this given A.P. has 27 terms in it.