Question

find the number of terms in an A.p given that it's 1st and last terms are a and 37a respectively, and that it's common difference is 49

Answer 1

last term is a + (n-1)d = 37a
36a = 49(n-1)
36a = 49n - 49
n = (36a+49)/49 or (36/49)a + 1

but n must be an integer, so a must be a multiple of 49
if a=49 , n = 37
if a = 98 , n = 73
if a = 147 , n = 109
etc
(n increases by 36)

check my second example, a = 98 , n = 73
terms would be 98 , 147, 196 , ...
term(71) = a + 72d = 98 + 72(49) = 3626
and 37a = 37(98) = 3626

Answer 2

If the sum of 8th and 9th terms of an arithematic prograssion is 72 and the 4th term is -6, find the common difference.

Answer 3

I need the solution pls