In an arithmetic progression, the 30th term is 389, and the 14th term is 181. Find the sum of the first 25 terms.

Guest Jun 22, 2020

#1**0 **

Formula for the n^{th} term of an arithmetic progression: t_{n} = t_{1} + (n - 1)d

---> 389 = t_{1} + (30 - 1)d ---> 389 = t_{1} + 29d

---> 181 = t_{1} + (14 - 1)d ---> 181 = t_{1} + 13d

Subtracting: 208 = 16d

13 = d

To find the first term: 181 = t_{1} + 13d ---> 181 = t_{1} + 13(13)

181 = t_{1} + 169

12 = t_{1}

Now, you know that t_{1} = 12 and d = 13,

use this formula to find the 25^{th} term: t_{n} = t_{1} + (n - 1)d

And use this formula to find the sum of the first 25 terms: Sum = n( t_{1} + t_{n} ) / 2

where n is the number of terms

t_{1} is the value of the first term

t_{n} is the value of the last term.

geno3141 Jun 22, 2020