# MAT - Paper 2011 - Q5

> Source: https://ollybritton.com/notes/maths/problems/mat/2011/q5/ · Updated: 2021-08-12 · Tags: mat, maths, notes

## Flashcards
##### What is the general $n$th term for a geometric sequence??
$$
U_n = ar^{n-1}
$$

##### How can you rewrite the formula for the sum of the sequence $U_n = 2^n$??
$$
U_n = 2 \cdot 2^{n-1}
$$

##### What is the formula for the sum of the sequence $U_n = 2^n$??
$$
2\left(2^n - 1\right)
$$

##### What is the formula for the sum of the sequence $U_n = 4^n$??
$$
\frac{4\left(4^n - 1\right)}{3}
$$

##### What is the formula for the sum of the sequence $U_n = 69^n$??
$$
\frac{69\left(69^n - 1\right)}{68}
$$

##### $$2 + 2^3 + 2^5$$ How could you formulate this as a more "standard" geometric sequence??
$$
U_n = 2\cdot4^{n}
$$

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