Question

find the common difference of an ap whose first term os 100 and the sum of whose first six term is five times the sum of the next sixterms ?

Answer 1

hello friend....
in this question ,we have to find the common defference

solution:-
shown in attachment

hence.
the common defference of A.P is = -10 answer

## hope it helps##

Answer 2

Answer:

d=-10

Step-by-step explanation:

Given a=100,

S6 = 5(S12 -S6)  

S6 = 5S12 -5S6

∴6S6 = 5S12...... eqn 1

Sn= n[2a+(n-1)d]/2

S6=6[2x100 + 5d]/2 = 600 + 15d

S12 = 12[2x100 + 11d]/2 = 1200 + 66d

Substituting the values in eqn 1

6[600 + 15d] = 5[1200 + 66d]

3600 + 90d = 6000 + 330d

330d - 90d = 3600 - 6000

240d = -2400

∴ d = -10