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AnilSinghBora
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Show that a1, a2 … , an , … form an AP where an is defined as below (i) an = 3+4n Q10.(1)

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How i solve the easiest way to solve the problem of arithmetic progressions of exercise of 5.3 of class 10th, how i solve in easy way Show that a1, a2 … , an , … form an AP where an is defined as below (i) an = 3+4n

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  1. an = 3+4n

    a1 = 3+4(1) = 7

    a2 = 3+4(2) = 3+8 = 11

    a3 = 3+4(3) = 3+12 = 15

    a4 = 3+4(4) = 3+16 = 19

    We can see here, the common difference between the terms are;

    a2 − a1 = 11−7 = 4

    a3 − a2 = 15−11 = 4

    a4 − a3 = 19−15 = 4

    Hence, ak + 1ak is the same value every time. Therefore, this is an AP with common difference as 4 and first term as 7.

    Now, we know, the sum of nth term is;

    Sn = n/2[2a+(n -1)d]

    S15 = 15/2[2(7)+(15-1)×4]

    = 15/2[(14)+56]

    = 15/2(70)

    = 15×35

    = 525

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