Question

7th term of an arithmetic sequence is 100 and 11th term is 140.
(i) What is fifteenth term of this sequence ?

Hint:

You can find the common difference d directly using the formula d = (am - aₙ)/(m-n). Here, d = a₁₁ - a₇11-7 = (140 - 100)/(4) = (40)/(4) = 10. This is faster than setting up and solving simultaneous equations.

Answer 1

We are given two terms of an arithmetic sequence and asked to find the 15th term.
Given: a₇ = 100 and a₁₁ = 140.

The n-th term of an arithmetic sequence is aₙ = a + (n-1)d. We can set up a system of two linear equations with two variables, a (the first term) and d (the common difference), and solve for them.

Using the formula aₙ = a + (n-1)d, we can write the given information as two equations:
For the 7th term: a₇ = a + (7-1)d = a + 6d = 100 --- (1)
For the 11th term: a₁₁ = a + (11-1)d = a + 10d = 140 --- (2)
To find d, we can subtract equation (1) from equation (2):
(a + 10d) - (a + 6d) = 140 - 100 4d = 40 d = (40)/(4) = 10 The common difference is 10.
Now, substitute d=10 back into equation (1) to find a:
a + 6(10) = 100 a + 60 = 100 a = 100 - 60 = 40 The first term is 40.
Now we can find the 15th term (a₁₅):
a₁₅ = a + (15-1)d a₁₅ = 40 + 14(10) a₁₅ = 40 + 140 a₁₅ = 180 The fifteenth term of the sequence is 180.