In an arithmetic progression, the 30th term is 389, and the 14th term is 181. Find the sum of the first 25 terms.
Formula for the nth term of an arithmetic progression: tn = t1 + (n - 1)d
---> 389 = t1 + (30 - 1)d ---> 389 = t1 + 29d
---> 181 = t1 + (14 - 1)d ---> 181 = t1 + 13d
Subtracting: 208 = 16d
13 = d
To find the first term: 181 = t1 + 13d ---> 181 = t1 + 13(13)
181 = t1 + 169
12 = t1
Now, you know that t1 = 12 and d = 13,
use this formula to find the 25th term: tn = t1 + (n - 1)d
And use this formula to find the sum of the first 25 terms: Sum = n( t1 + tn ) / 2
where n is the number of terms
t1 is the value of the first term
tn is the value of the last term.