Geometric sequence 3

In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.

Correct result:

a1 =  4
q =  5
n =  9

Solution:

a8=a1q7=312500 a11=a1q10=39062500  31250039062500=q7q10  0.008=q−3 0.008−0.333333333333=q q=5  a8=a1q7=a1⋅57=312500 a1=31250057=4
 sn=1953124=a1qn−1q−1=5n−15−1 1953124=5n−1 1953125=5n ln⁡1953125=nln⁡5  n=ln⁡1953125ln⁡5 n=9

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