Question

The sum of the first 6 terms of a geometric series is 15,624 and the common ratio is 5. What is the first term of series?

Answer 1

4

Explanation:

Suppose

• S = sum of the six terms
• a1 = the first term

`\left. { S = a _ { 1 } \frac { 1 - 5 ^ { 6 } } { 1 - 5 } } \\\\ { \Leftrightarrow S = \frac { a _ { 1 } } { 4 } ( 5 ^ { 6 } - 1 ) } \\\\ { \Leftrightarrow a _ { 1 } = \frac { 4 S } { 5 ^ { 6 } - 1 } } \right.`

then a1 = (4×15 624)÷(5^(6)-1)

= 4