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Find the first four terms of an arithmetic progression (AP) given the first term (a) and the common difference (d) for the following cases: i) a=10, d=10; ii) a=-2, d=0; iii) a=4, d=-3; iv) a=-1, d=1/

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Answers

5 parts
i
10, 20, 30, 40
ii
-2, -2, -2, -2
iii
4, 1, -2, -5
iv

−1,−12,0,12-1, -\frac{1}{2}, 0, \frac{1}{2}

v
-1.25, -1.50, -1.75, -2.00

Step-by-step solution

20 steps

To find the first four terms of an AP, we use the formula for the nn-th term: an=a+(n−1)da_n = a + (n-1)d, or simply add the common difference dd to the previous term.

Part i· 4 steps

a=10,d=10a=10, d=10

  1. First term.

    a1=a=10a_1 = a = 10

  2. Second term.

    a2=a1+d=10+10=20a_2 = a_1 + d = 10 + 10 = 20

  3. Third term.

    a3=a2+d=20+10=30a_3 = a_2 + d = 20 + 10 = 30

  4. Fourth term.

    a4=a3+d=30+10=40a_4 = a_3 + d = 30 + 10 = 40

    The first four terms are 10,20,30,40\boxed{10, 20, 30, 40}.

Part ii-2, -2, -2, -2

a=−2,d=0a=-2, d=0

  1. First term.

    a1=a=−2a_1 = a = -2

  2. Second term.

    a2=a1+d=−2+0=−2a_2 = a_1 + d = -2 + 0 = -2

  3. Third term.

    a3=a2+d=−2+0=−2a_3 = a_2 + d = -2 + 0 = -2

  4. Fourth term.

    a4=a3+d=−2+0=−2a_4 = a_3 + d = -2 + 0 = -2

    The first four terms are −2,−2,−2,−2\boxed{-2, -2, -2, -2}.

Part iii4, 1, -2, -5

a=4,d=−3a=4, d=-3

  1. First term.

    a1=a=4a_1 = a = 4

  2. Second term.

    a2=a1+d=4+(−3)=1a_2 = a_1 + d = 4 + (-3) = 1

  3. Third term.

    a3=a2+d=1+(−3)=−2a_3 = a_2 + d = 1 + (-3) = -2

  4. Fourth term.

    a4=a3+d=−2+(−3)=−5a_4 = a_3 + d = -2 + (-3) = -5

    The first four terms are 4,1,−2,−5\boxed{4, 1, -2, -5}.

Part iv

−1,−12,0,12-1, -\frac{1}{2}, 0, \frac{1}{2}

a=−1,d=12a=-1, d=\frac{1}{2}

  1. First term.

    a1=a=−1a_1 = a = -1

  2. Second term.

    a2=a1+d=−1+12=−22+12=−12a_2 = a_1 + d = -1 + \frac{1}{2} = -\frac{2}{2} + \frac{1}{2} = -\frac{1}{2}

  3. Third term.

    a3=a2+d=−12+12=0a_3 = a_2 + d = -\frac{1}{2} + \frac{1}{2} = 0

  4. Fourth term.

    a4=a3+d=0+12=12a_4 = a_3 + d = 0 + \frac{1}{2} = \frac{1}{2}

    The first four terms are −1,−12,0,12\boxed{-1, -\frac{1}{2}, 0, \frac{1}{2}}.

Part v-1.25, -1.50, -1.75, -2.00

a=−1.25,d=−0.25a=-1.25, d=-0.25

  1. First term.

    a1=a=−1.25a_1 = a = -1.25

  2. Second term.

    a2=a1+d=−1.25+(−0.25)=−1.50a_2 = a_1 + d = -1.25 + (-0.25) = -1.50

  3. Third term.

    a3=a2+d=−1.50+(−0.25)=−1.75a_3 = a_2 + d = -1.50 + (-0.25) = -1.75

  4. Fourth term.

    a4=a3+d=−1.75+(−0.25)=−2.00a_4 = a_3 + d = -1.75 + (-0.25) = -2.00

    The first four terms are −1.25,−1.50,−1.75,−2.00\boxed{-1.25, -1.50, -1.75, -2.00}.

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