Question

✨LOTS OF POINTS✨

For each sequence write an explicit formula: 7. 1,5, 25, ... a_1:___ r/d:___ a_n:___
8. 29, 35, 41, ... a_1:___ r/d:___ a_n:___

For this sequence, write a recursive formula 9. 7,49,343, ... r/d:___ a_n:___​

Answer 1

• Q7. a₁ = 1 , r = 5, aₙ = 5ⁿ⁻¹
• Q8. a₁ = 29, d = 6, aₙ = 6n + 23
• Q9. a₁ = 7, r = 7, aₙ = 7aₙ₋₁

Explanation:

Q7.

Given sequence

• 1, 5, 25, ...

This is a GP with the first term of a₁ = 1 and common ratio r = 5

Explicit formula is:

• aₙ = 1*5ⁿ⁻¹= 5ⁿ⁻¹

Q8.

Given sequence

• 29, 35, 41, ...

This is an AP with the first term of a₁ = 29 and common difference d = 6

Explicit formula:

• aₙ = 29 + 6(n - 1) = 29 + 6n - 6 = 6n + 23

Q9.

Given sequence

• 7, 49, 343, ...

This is a GP with the first term a₁ = 7 and common ratio r = 7

Recursive formula is:

• aₙ = aₙ₋₁*7 = 7aₙ₋₁