The first ter of an Ap is equal to twice the common difference d.find in terms of d,the 5th term of the A.p

Mathematics

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Answer

6d

Step-by-step solution

4 steps
  1. Recall the formula for the nth term of an AP

    The formula for the nth term of an Arithmetic Progression (AP) is given by:
    an=a1+(n−1)da_n = a_1 + (n-1)d
    where ana_n is the nth term, a1a_1 is the first term, and dd is the common difference.

  2. Use the given information

    We are given that the first term (a1a_1) is equal to twice the common difference (dd):
    a1=2da_1 = 2d

  3. Find the 5th term (a5a_5)

    Substitute n=5n=5 into the formula for the nth term:
    a5=a1+(5−1)da_5 = a_1 + (5-1)d
    a5=a1+4da_5 = a_1 + 4d

  4. Substitute the expression for a1a_1 into the equation for a5a_5

    Substitute a1=2da_1 = 2d into the equation for a5a_5:
    a5=(2d)+4da_5 = (2d) + 4d
    a5=6da_5 = 6d

    The 5th term of the AP in terms of dd is:
    6d6d

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