# Sequences AP + GP

The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members.

Correct result:

a1 =  8
b1 =  10
c1 =  12
a2 =  17
b2 =  10
c2 =  3
g1 =  3
g2 =  6
g3 =  12
k1 =  12
k2 =  6
k3 =  3

#### Solution:

Our quadratic equation calculator calculates it.

${b}_{1}=b=10$
${c}_{1}=b+{d}_{1}=10+2=12$
${a}_{2}=b-{d}_{2}=10-\left(-7\right)=17$
${b}_{2}=b=10$
${c}_{2}=b+{d}_{2}=10+\left(-7\right)=3$
${g}_{1}={a}_{1}-5=8-5=3$
${g}_{2}=b-4=10-4=6$
${g}_{3}={c}_{1}=12$
${k}_{1}={a}_{2}-5=17-5=12$
${k}_{2}=b-4=10-4=6$

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