Question

In an arithmetic sequence, the 1st term is 7, and the 6th term is 32. What is the 20th term of this sequence?

• A. 97
B. 228
0 c. 107
• D. 102

Answer 1

The answer is D

To find the 20th term of an arithmetic sequence, we need to determine the common difference (d) first.

In an arithmetic sequence, the difference between any two consecutive terms is constant.

Given that the 1st term (a₁) is 7 and the 6th term (a₆) is 32, we can use these values to find the common difference.

The formula to find the nth term (aₙ) of an arithmetic sequence is:
aₙ = a₁ + (n - 1) * d

Substituting the values we have:
a₁ = 7
a₆ = 32

Using the formula for the 6th term:
32 = 7 + (6 - 1) * d
32 = 7 + 5d

Simplifying the equation:
32 - 7 = 5d
25 = 5d
d = 5

Now that we know the common difference (d = 5), we can find the 20th term (a₂₀) using the formula:
a₂₀ = a₁ + (20 - 1) * d

Substituting the values we have:
a₁ = 7
d = 5
n = 20

a₂₀ = 7 + (20 - 1) * 5
a₂₀ = 7 + 19 * 5
a₂₀ = 7 + 95
a₂₀ = 102

Therefore, the 20th term of the arithmetic sequence is 102.

【Answer】: D. 102

Answer 2

`\sf\\\textsf{The nth term of an arithmetic sequence is given by:}\\t_n=a+(n-1)d\\\textsf{where, a is first term, n is number of terms, d is common difference and }t_n\textsf{ is the }\\\textsf{nth term of the sequence.}\\According\ to\ the\ question,\\\textsf{1st term(a)}=7\\\textsf{6th term}(t_6)=32\\Now,\\t_6=32\\or,\ a+5d=32\\or,\ 7+5d=32\\or,\ 5d=25\\or,\ d=5\\\therefore\ \textsf{20th term of the sequence = }t_(20)=a+(20-1)d=7+19(5)=102`