if the sum of first four terms of an AP IS P AND THE SUM OF FIRST 8 TERMS IF - Maths - Sequences and Series

Question

if the sum of first four terms of an AP IS P AND THE SUM OF
FIRST 8 TERMS IF IS Q AND SUM OFfirst 12 terms is r express 3p+r in
terms of q

Vipin Verma · Accepted Answer

Sum of n terms of AP is
Sn=n2[2a+(n-1)d]
Then,
S4=42[2a+3d]P=2[2a+3d]P=4a+6d (1)

S8=82[2a+7d]Q=4[2a+7d]Q=8a+28d (2)

S12=122[2a+11d]R=6[2a+11d]R=12a+66d (3)

Now,3P+R=3[4a+6d]+12a+66d=12a+18d+12a+66d=24a+84d=3(8a+28d)=3QSo,
3P+R=3Q

if the sum of first four terms of an AP IS P AND THE SUM OF FIRST 8 TERMS IF IS Q AND SUM OFfirst 12 terms is r. express 3p+r in terms of q