Problem: Given a geometric sequence with the first term ξ =0 and rξ =0 and an arithmetic sequence with the first term =0. A third sequence 1,1,2,β¦ is formed by adding corresponding terms of the two given sequences. The sum of the first ten terms of the third sequence is.
Answer Choices:
A. 978
B. 557
C. 467
D. 1068
E. not possible to determine from the information given.
Solution:
Let the two series be a,ar,ar2,β― and 0,d,2d,β―,a+0=1;
β΄a=1 and r+d=1,r2+2d=2.β΄r=2,d=β1.
S1β=rβ1a(rnβ1)β=2β11(210β1)β=1023,
S2β=2nβ[0+(nβ1)d]=210β[0+9(β1)]=β45.
β΄S=1023β45=978.