The sum of first 8 term of an AP is 100 and sum of first 19 terms is 551. Find the AP..?

1 Answer
Mar 25, 2018

#2, 5, 8, 11, 14, ............................................#

Explanation:

First we will list the data we are given.

The sum of the first 8 terms of the A.P is = #100#.

The sum of the first 19 terms is = #551#.

Now Let The First term of the A.P be #a#, and the common difference be #d#.

So, According to the problem,

#color(white)(xxx)8/2[a + a + (8 - 1) d] = 100#

#rArr 4[2a + 7d] = 100#

#rArr 2a + 7d = 25#........................................(i)

And, #19/2[a + a + (19 - 1)d] = 551#

#rArr 19/2 [2a + 18d] = 551#

#rArr 19[a + 9d] = 551#

#rArr a + 9d = 29#..........................(ii)

Now, Just Solve For #a# and #d#.

FIrst, Multiply eq(ii) with #2#.

So, we get,

#2a + 18d = 58#............................(iii)

Now. Subtract eq(i) from eq(iii).

So, We get,

#color(white)(xxx)cancel(2a) + 18d cancel(- 2a) - 7d = 58 - 25#

#rArr 11d = 33#

#rArr d = 3#

Now, Substitute #d = 3# in eq(i).

So, We get,

#color(white)(xxx)2a + 7 * 3 = 25#

#rArr 2a + 21 = 25#

#rArr 2a = 25 - 21#

#rArr 2a = 4#

#rArr a = 2#

So, Now we can form the A.P.

The AP will be #a, a + d, a + 2d, a + 3d,............................,a + (n - 1)d.#

So, The Finalised A.P. is :-

#2, 5, 8, 11, 14, ............................................#