Find the 6th term of the sequence $\frac{2}{3} \frac{7}{15} \frac{4}{15}$,...

Analyze the question

The sequence is 2/3, 7/15, 4/15, ... Convert to a common denominator of 15 to see the pattern.

Concept

If the differences between consecutive terms are constant, the sequence is an arithmetic progression (AP) with nth term: Tₙ = a + (n − 1)d

Solution

Write each term over 15:

• T₁ = 2/3 = 10/15
• T₂ = 7/15
• T₃ = 4/15

Common difference: d = 7/15 − 10/15 = −3/15 = −1/5 Check: 4/15 − 7/15 = −3/15 ✓

Now find the 6th term: T₆ = a + 5d T₆ = 10/15 + 5(−3/15) T₆ = 10/15 − 15/15 T₆ = −5/15 = −1/3

Answer

The 6th term is −1/3, which is option A.

Tip

When a sequence has fractions with different denominators, first convert them all to the same denominator. The pattern in the numerators (10, 7, 4, ... decreasing by 3) then becomes obvious: 10, 7, 4, 1, −2, −5, so the 6th term is −5/15 = −1/3.