A geometric sequence has a sum to infinity of –3 - AQA - A-Level Maths Pure - Question 3 - 2021 - Paper 1

The sum to infinity of a geometric series can be expressed as:

$S = \frac{a}{1 - r}$

where:

• S is the sum to infinity,
• a is the first term,
• r is the common ratio.

Given that the original sequence has a sum to infinity of –3, if we multiply each term by –2, the new sum becomes:

$S_{new} = (-2) \cdot S_{original}$

Substituting the original sum:

$S_{new} = -2 \cdot (-3) = 6$

Thus, the sum to infinity of the new sequence is 6.