Question

If the sum of first 18 terms of an AP is 639 and
its first term is 10, find the 25th term.​

Answer 1

Given:-

Sum of 18 terms of an A.P. is 639.

First term = 10

To find:-

25th term

Solution:-

We know,

$\sf{S_n = \dfrac{n}{2}[2a+(n-1)d]}$

= $\sf{S_{18} = \dfrac{18}{2}[2\times10 + (18-7)d]}$

$\sf{\implies 639 = 9[20 + 17d]}$

$\sf{\implies \dfrac{639}{9} = 20 + 17d}$

$\sf{\implies 71 = 20 + 17d}$

$\sf{\implies 71-20 = 17d}$

$\sf{\implies 51 = 17d}$

$\sf{\implies d = \dfrac{51}{17}}$

$\sf{\implies d = 3}$

Now,

First term (a) = 10

Common difference (d) = 3

= $\sf{a_n = a + (n-1)d}$

= $\sf{a_{25} = 10 + (25-1)\times3}$

= $\sf{a_{25} = 10 + 24\times3}$

= $\sf{a_{25} = 10+72}$

= $\sf{a_{25} = 82}$

$\sf{\therefore}$ The 25th term is 82.

Note:-

• a = First term
• l = last term
• d = Common difference