9th term = 52 ---> a + 8d = 52
12th term = 70 --> a + 11d = 70
subtract them
3d = 18
d = 6
then a+48 = 52
a = 4
20th term = a + 19d = 4 + 114 = 118
12th term = 70 --> a + 11d = 70
subtract them
3d = 18
d = 6
then a+48 = 52
a = 4
20th term = a + 19d = 4 + 114 = 118
a+8d=52
12th term = 70
a+11d =70
Subtract them
a+8d=52
-
a+11d =70
3d=18
d=6 buy dividing both side by 3
To fine a
a+8d=52
When d= 6
a+8(6)=52
a+48=52
a=52-48
a=4
Then the sum of 20th term
Will be
S20= n/2[2a + (n-1)d]
S20= 20/2[2(4) + (20-1)6]
S20=10[8+19(6)]
S20=10[8+114]
S20=10[122]
S20=1220 answer
Chiemerie
In an AP, each term is obtained by adding the common difference to the previous term.
Let's label the 9th term as a₁ and the common difference as d. According to the information given, a₁ = 52.
So, the 12th term (a₄) will be a₁ + 3d = 52 + 3d = 70.
Simplifying this equation, we get:
3d = 70 - 52
3d = 18
d = 18/3
d = 6
Now that we have the common difference (d = 6), we can find the 20th term (a₂₀) using the formula:
a₂₀ = a₁ + (n - 1)d
where n is the term number.
Plugging in the values, we have:
a₂₀ = 52 + (20 - 1) * 6
= 52 + 19 * 6
= 52 + 114
= 166
Therefore, the 20th term of the AP is 166.
To find the sum of the first n terms of an arithmetic progression, you can use the formula:
Sn = (n/2)(2a₁ + (n - 1)d)
where Sn represents the sum of the first n terms.
Using this formula, we can find the sum of the first 20 terms (S20) as follows:
S20 = (20/2)(2 * a₁ + (20 - 1) * d)
= 10(2 * 52 + 19 * 6)
= 10(104 + 114)
= 10(218)
= 2180
Therefore, the sum of the 20 terms of the AP is 2180.