the value of the term lying between the 1st and 99th term of an a.p is 100 . the value of 99th term is 198 . find the value of first term
Answers
Given : the value of the term lying between the 1st and 99th term of an a.p is 100 . the value of 99th term is 198
To find : the value of first term
Solution:
a = first term
a + (n-1)d = 100 Eq 1
a + (99-1)d = 198 Eq 2
Eq2 - Eq1
=> (99 - n) d = 98
98 = 1 * 98 = 2 * 49 = 7 * 14
d can be 1 , 2 , 7 , 14 , 98
Substitute value of d in eq2
d = 1 => a = 100 ( 100 can not be 1st term as 100 lying between 1st & 99th terms)
d = 2 => a = 2
d = 7 => a = - 488
d = 14 => a = -1174
d = 49 => a = -4604
d = 98 => a = -9406
if we talk about only +ve values
then 1st term = 2
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