Question

7th term of an arithmetic sequence is 100 and 11th term is 140.
(ii) What is the third term of this sequence ?

Hint:

Once you know any term and the common difference, you can find any other term easily. Use the relation am = aₙ + (m-n)d. To find a₃ from a₇, calculate a₃ = a₇ + (3-7)d = 100 + (-4)(10) = 60. This avoids the need to find the first term, a.

Answer 1

Using the same arithmetic sequence from the previous part, where a₇ = 100 and a₁₁ = 140, we need to find the 3rd term (a₃).

We will use the first term a and common difference d that were calculated in the previous part. 
From part (i), we found a = 40 and d = 10. 
The formula for the n-th term is aₙ = a + (n-1)d.

We need to find the third term, a₃. 
Using the formula with n=3, a=40, and d=10: 
a₃ = a + (3-1)d a₃ = 40 + 2(10) a₃ = 40 + 20 a₃ = 60 

Alternative Method: 
We know a₇ = 100 and d=10. We can work backwards to find a₃. 
a₃ = a₇ - (7-3)d 
a₃ = 100 - 4d 
a₃ = 100 - 4(10) = 100 - 40 = 60.

The third term of the sequence is 60.