Question

Find the specified partial sum of a1 = 32; ₫ = 4; S26

Answer 1

The 26th partial sum (S26) of the arithmetic sequence with a1 = 32 and d = 4 is 2132, calculated using the formula for the sum of the first n terms of an arithmetic sequence.

Step-by-step explanation:

The student is asking to find the 26th partial sum of an arithmetic sequence, where the first term a1 is 32 and the common difference d is 4. To find the specified partial sum S26, we can use the formula for the sum of the first n terms of an arithmetic sequence, which is Sn = n/2(2a1 + (n - 1)d).

Let's substitute the given values into this formula:

1. First, identify the first term a1 as 32
2. Second, identify the common difference d as 4
3. Third, since we are looking for S26, set n to 26
4. Now substitute these values into the formula to calculate the partial sum:

S26 = 26/2 [2(32) + (26 - 1)(4)]
S26 = 13 [64 + 100]
S26 = 13 [164]
S26 = 2132

Therefore, the 26th partial sum of the sequence is 2132.