Asked by Jamiu
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
i. 1st term
ii. common difference
iii. sum of the first 30 terms
Answers
Answered by
Reiny
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
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
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