Question

Find t15 for an arithmetic sequence where: t3 = -4+5i and t6 = -13+11

Answer 1

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Answer 2

Answer:

as we know tn=a+(n-1)d

t3=a+(3-1)d=a+2d

so a+2d=-4+5i... (1)

similarly t6=a+(6-1)d=a+5d

so a+5d=-13+11i.. (2)

subtracting equation (1) from (2) we get,

3d= -9+6i

so d= -3+2i

putting the value of d in equation (1)

a+2 (-3+2i)= -4+5i

a-6+4i= -4+5i

so a=2+i

therefore t15=a+(15-1)d=a+14d

so t15=(2+i)+14 (-3+2i)=2+i-42i+28i=2-13i