the 9th term of an AP is 52 while the 12th term is 70. find the sum of it's 20th term?
9th term = 52
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
Since is sum of 20th term not the 20th term then the answer is 1220
Gud subject maths
Not a correct answer
The 9th and 12th terms of an AP are 50 and 65 respectively.find (a) the common difference (b) the sum of it's first 70 terms
Since
Chiemerie
To find the sum of the 20th term of an arithmetic progression (AP), we first need to determine the common difference.
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.
I love Osinachi
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