Mathematics

Question

Find the fifth term of the arithmetic sequence in which t1 = 3 and tn = tn-1 + 4. A) 5 B) 7 C) 19 D) 23 2) Find the tenth term of the arithmetic sequence in which t1 = 2 and t4 = -10. A) -10 B) -34 C) -38 D) -106 3) Find the fifth term of the geometric sequence in which t1 = 3 and tn = 2tn-1. A) 5 B) 6 C) 48 D) 96

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1 Answer

  • we know that

    Part a) Find the fifth term of the arithmetic sequence in which t1 = 3 and tn = tn-1 + 4
    t1=3
    t2=t1+4----> 3+4-----> 7
    t3=t2+4-----> 7+4----> 11
    t4=t3+4-----> 11+4---> 15
    t5=t4+4-----> 15+4---> 19

    the answer Part a) is 19

    Part b)     Find the tenth term of the arithmetic sequence in which t1 = 2 and t4 = -10

    we know that 
    tn=t1+(n-1)*d-----> d=[tn-t1]/(n-1)
    t1=2
    t4=-10
    n=4
    find the value of d
    d=[-10-2]/(4-1)-----> d=-12/3----> d=-4
    find the     tenth term (t10)
    t10=t1+(10-1)*(-4)----> t10=2+9*(-4)----> t10=-34

    the answer Part b) is -34

    Part c) Find the fifth term of the geometric sequence in which t1 = 3 and tn = 2tn-1
    t1=3
    t2=2*t1----> 2*3----> 6
    t3=2*t2----> 2*6----> 12
    t4=2*t3-----> 2*12---> 24
    t2=2*t4----> 2*24----> 48

    the answer Part c) is 48