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in Arithmetic Progression by (49.2k points)
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The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

1 Answer

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by (50.7k points)
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Best answer

Given:

a4 = 3a1 …(i)

a7 = 2a3 +1 …(ii)

We know

an = a + (n -1) d

So,

a3 = a +2d

a4 = a +3d

a7 = a +6d

Put all the values of a1 and a4 in (i),

a + 3d = 3a

⇒ 3d = 3a - a

⇒ 3d = 2a

⇒ d = \(\frac{2a}{3}\)

Put all the values of a7 and a3 in (ii),

⇒ a + 6d =  2(a +2d) +1

 a + 6d = 2a + 4d + 1

⇒ 6d - 4d = 2a - a +1

⇒ 2d = a +1

⇒ d = 2

Hence, first term is 3 and the common difference is 2.

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