Find the seventh term of Arithmetic sequence with 27th, 28th and 29th terms 196, 203 and 210 respectively
Answers
Answer: 56
Solution:
Let the given arithmetic sequence be,
a , a + d , a + 2d , ... a + (n - 1)d
Where, a and d are the first term and common difference of the Arithmetic sequence respectively.
Now, we know,
=> nth term of AP = a + (n - 1)d
Regarding this Arithmetic sequence, 27th term is 196.
=> a + (27 - 1)d = 196
=> a + 26d = 196
=> a = 196 - 26d ...(1)
We know, Common difference is the difference between consecutive terms and is same for the sequence.
Hence,
=> Common difference, d = 28th term - 27th term = 29th term - 28th term
=> d = 203 - 196 = 210 - 203
=> d = 7
Now, we have
- Common difference, d = 7
Substituting the value of d in (1), we get a,
=> a = 196 - 26×7
=> a = 196 - 182
=> a = 14
Hence, The first term is a = 14 while the common difference is d = 7.
So, the seventh term is given by,
=> a + (7 - 1)d
=> a + 6d
=> 14 + 6×7
=> 14 + 42
=> 56
Therefore, Seventh term of the Arithmetic sequence is 56.