d 9th term of an Ap is 52 while d 12th term is 70. find sum of it's 20th term?
Just answered you previous post of the same question.
BTW, "find the sum of it's 20th term" is confusing.
I found the 20th term.
If you want the sum of the first 20 terms, use the values of a and d I found for you and use the formula.
To find the sum of the 20th term of an Arithmetic Progression (AP), we need to first find the common difference (d) and then use the formula for the sum of an AP.
Given that the 9th term is 52 and the 12th term is 70, we can find the common difference (d) by subtracting the 9th term from the 12th term:
d = 70 - 52
d = 18
Now, we can use the formula for the sum of an AP to find the sum of the 20th term:
Sn = (n/2) * (2a + (n-1)d)
where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
In this case, we want to find the sum of the 20th term, so n = 20. We already know the first term (a) is not given, but we can calculate it.
To find the first term, we can use the formula:
a = d - (n-1)d
a = 52 - (9-1) * 18
a = 52 - 8 * 18
a = 52 - 144
a = -92
Now that we have the first term (a), common difference (d), and number of terms (n), we can substitute them into the sum formula:
S20 = (20/2) * (2 * -92 + (20-1) * 18)
S20 = 10 * (-184 + 19 * 18)
S20 = 10 * (-184 + 342)
S20 = 10 * 158
S20 = 1580
Therefore, the sum of the 20th term of the given AP is 1580.