Question

1. The sum of first 21 terms of an A.P. is 28 and the sum of the
1st 28 terms is 21. Show that one term of the progression
is zero and find the sum of the preceding terms.​

Answer 1

Answer:

Step-by-step explanation:

28=t1+⋯+t21=21⋅t11 and −7=t22+⋯+t28=7⋅t25.

Hence t11=43 and t25=−1, and so d=t25−t1125–11=−16. Thus, −6d=1, and 0=t25−6d=t19.

Therefore,

t1+⋯+t18=t1+⋯+t19=19⋅t10=19⋅(−9d)=572 .

The 19th term is 0, and the sum of the first 18 terms is 572. ■