The 25 term of an Arithmetic Progression is 7 1/2 and the sum of the first 23 terms is 98 1/2. Find the

i. 1st term
ii. common difference
iii. sum of the first 30 terms

1 answer

25th term = 7 1/2
a + 24 d = 15/2

sum of first 23 terms = 98 1/2
(23/2)(2a + 22d) = 197/2
23(2a+22d) = 197
2a+22d = 197/23
a+11d = 197/46
subtract the two equations
13d = 15/2 - 197/46 = 74/23
d = 74/299

sub back into first equation
a + 24(74/299) = 15/2
a = 933/598

so sum of 30 terms
= 15(2(933/598) + 29(74/299) )
= 92340/598

sure was expecting some nicer numbers, better check my arithmetic