Question

The first term of an AP is equal to twice the forth term. Then find the ratio of common difference and first term (d/a1).
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Answer 1

Step-by-step explanation:

Given:-

The first term of an AP is equal to twice the fourth term.

To find:-

Find the ratio of common difference and first term

Solution:

Let the first term of an AP = a1

Common difference of the AP = d

We know that

The general term or nth term of an AP

an = a+(n-1)d

Fourth term of the AP = a4

a4 = a1 + (4-1)d

=>a4 = a1 +3d

Now given that

First term = Twice the fourth term

=>a1 = 2× a4

=>a1 = 2×(a1+3d)

=>a1 = 2a1 +6d

=>a1 - 2a1 = 6d

=> -a1 = 6d

=>a1 = -6d

=>a1/d = -6

=>d/a1 = -1/6

=>d : a1 = -1:6

Answer:-

d/a1 = -1/6

The ratio of the common difference and the first term = -1:6

Used formula:-

The general term or nth term of an AP

an = a+(n-1)d

Where , a is the first term ,n is the

number ofterms and d is the common

difference of an AP