Question

Please help! 25 points! Find the sum of the first 6 terms of the following series, to the nearest integer.

28, 112, 448,....

Answer 1

595

Explanation:

First term:

7

7 ⋅ 4 = 28

Second term:

28

28 ⋅ 4 = 112

Third term:

112

112 ⋅ 4 = 448

Fourth term:

448

This geometric sequence can be further described by the equation:

aₙ = 7 ⋅ 4 ⁿ⁻¹

So if you want to find the 4th term, n = 4

a ₄ = 7 ⋅ 4 ⁴⁻¹ = 7 ⋅ 4 ³ = 7 ⋅ 64 = 448

Note:

aₙ = a₁ rⁿ ⁻¹

Answer 2

The sum of the first 6 terms of the series is 38220

Finding the sum of the first 6 terms of the series

From the question, we have the following parameters that can be used in our computation:

28, 112, 448,....

In the above sequence, we can see that 4 is multiplied to the previous term to get the new term

So, we have the first 6 terms to be

28, 112, 448, 448 * 4, 448 * 4 * 4, 448 * 4 * 4 * 4

Evaluate

28, 112, 448, 1792, 7168, 28672

Add these terms

Sum of first 6 = 28 + 112 + 448 + 1792 + 7168 + 28672

Sum of first 6 = 38220

Hence, the sum of the first 6 terms of the series is 38220