find the common difference of an AP whose first term is 5 and the sum of its form term is - Maths - Arithmetic Progressions

Question

find the common difference of an AP whose first term is 5 and
the sum of its form term is half the sum of its 4 term is half the
sum of the next four term?

Manbar Singh · Accepted Answer

Let a be the first term and d be the common difference
We know that, sum of first n terms is given by,Sn = n22a+n-1dNow, sum of first 4 terms is,     S4 = 422a + 3d⇒S4 = 4a + 6d⇒S4 = 20 + 6d      as, a = 5Now, sum of next 4 terms = S8 - S4⇒sum of next 4 terms = 822a + 7d - 20 + 6d⇒sum of next 4 terms = 410+7d - 20 - 6d⇒sum of next 4 terms = 40 + 28d - 20 - 6d⇒sum of next 4 terms = 20 + 22dNow,        S4 = 12sum of next 4 terms⇒ 20 + 6d = 1220+22d⇒40 + 12d = 20 + 22d⇒10d = 20⇒d = 2

find the common difference of an AP whose first term is 5 and the sum of its form term is half the sum of its 4 term is half the sum of the next four term?