Question

Sum of first n terms of an arithmetic sequence is 5n²+2n. What is the 21st term of this sequence?

• A. 102
• B. 107
• C. 202
• D. 207

Answer 1

Answer:

D. 207

The 21st term of the sequence is 207.

The sum of the first $n$ terms is given by the formula:
$S_n = 5n^2 + 2n$

To find the 21st term ($t_{21}$), you subtract the sum of the first 20 terms ($S_{20}$) from the sum of the first 21 terms ($S_{21}$):
$t_{21} = S_{21} - S_{20}$

Step 1: Find $S_{21}$ (Substitute $n = 21$)
$S_{21} = 5(21)^2 + 2(21)$
$S_{21} = 5(441) + 42$
$S_{21} = 2205 + 42 = 2247$

Step 2: Find $S_{20}$ (Substitute $n = 20$)
$S_{20} = 5(20)^2 + 2(20)$
$S_{20} = 5(400) + 40$
$S_{20} = 2000 + 40 = 2040$

Step 3: Calculate the 21st term
$t_{21} = 2247 - 2040 = 207$