Question -
Answer -
(i) 7, 13, 19, …,205
Solutions:
(i) Given, 7, 13,19, …, 205 is the A.P
Therefore
First term, a = 7
Common difference, d = a2 − a1 =13 − 7 = 6
Let there are n terms in thisA.P.
an = 205
As we know, for an A.P.,
an = a + (n − 1) d
Therefore, 205 = 7 + (n − 1) 6
198 = (n − 1) 6
33 = (n − 1)
n = 34
Therefore, this given series has 34 terms init.
First term, a = 18
Common difference, d = a2-a1 =
d = (31-36)/2 = -5/2
Let there are n terms in this A.P.
an = 205
As we know, for an A.P.,
an = a+(n−1)d
-47 = 18+(n-1)(-5/2)
-47-18 = (n-1)(-5/2)
-65 = (n-1)(-5/2)
(n-1) = -130/-5
(n-1) = 26
n = 27
Therefore, this given A.P. has 27 terms in it.