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The 4th term of an A.P. is three times the first and the 7th term excessds twice the third term by 1. Find the first term 'a' and common difference 'd'.
  • a)
    a = 3, d = 2
  • b)
    a = 4, d = 3
  • c)
    a = 5, d = 4
  • d)
    a = 6, d = 5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The 4thterm of an A.P. is three times the first and the 7thterm excess...
Given: 4th term = 3 times the first term, 7th term = 2 times the third term + 1

Let's assume the first term is 'a' and the common difference is 'd'

Calculating the 4th term:
4th term = a + (4-1)d
4th term = a + 3d

Given, 4th term = 3a
So, a + 3d = 3a
2a = 3d
a/d = 2/3 ----(1)

Calculating the 7th term:
7th term = a + (7-1)d
7th term = a + 6d

Given, 7th term = 2*3rd term + 1
a + 6d = 2(a + 2d) + 1
a + 6d = 2a + 4d + 1
a = 2d - 1 ----(2)

Solving equations (1) and (2), we get:
a = 3, d = 2

Therefore, the first term is 3 and the common difference is 2. So, option 'A' is the correct answer.
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Community Answer
The 4thterm of an A.P. is three times the first and the 7thterm excess...
Option a is the correct answer

3,5,7,9,11,13,15,
4 th term means 9 it is 3 times of the 1 st term and 7th term 2 more times exceeds the 3 rd term by 1 by this we can conclude a=3 and d=2
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The 4thterm of an A.P. is three times the first and the 7thterm excessds twice the third term by 1. Find the first term a and common difference d.a)a = 3, d = 2b)a = 4, d = 3c)a = 5, d = 4d)a = 6, d = 5Correct answer is option 'A'. Can you explain this answer?
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