Question

The sum of first 3 terms of an arithmetic sequence is 30 and the sum of first 7 terms is 140.
(iii) Write the first three terms of this sequence.

Hint:

When asked for the terms of a sequence, the fundamental goal is always to find the first term (a) and the common difference (d). Once you have these two values, you can generate any term in the sequence.

Answer 1

Using the same AP as before (S₃=30, S₇=140), we need to write out the first three terms (a₁, a₂, a₃).

We have already found the constituent parts of the sequence:
- First term a = 5.
- Common difference d = 5.
- Second term a₂ = 10.
The terms of an AP are a, a+d, a+2d, ....

From the previous parts, we determined:
The first term a₁ = a = 5.
The second term a₂ = a + d = 5 + 5 = 10.
The third term a₃ can be calculated as a₂ + d.
a₃ = 10 + 5 = 15 Alternatively, using the formula:
a₃ = a + 2d = 5 + 2(5) = 5 + 10 = 15 So the first three terms are 5, 10, and 15.
We can check our work. The sum of these three terms is 5 + 10 + 15 = 30, which matches the given S₃ = 30.

The first three terms of the sequence are 5, 10, 15.