The 9th and 22nd term of an ap area 29 and 58 respectively find the sum of its first 70 term
13d = 29
now you have d, and you know that a+8d = 29
S70 = 70/2(2a+69d)
To find the sum of an arithmetic progression (AP), you need to know the first term, the common difference, and the total number of terms. In this case, we are given the 9th and 22nd terms, so we can find the common difference, and then calculate the sum of the first 70 terms.
First, let's find the common difference (d):
d = 22nd term - 9th term
d = 58 - 29
d = 29
Now that we have the common difference, we can find the first term (a) using the 9th term and the common difference:
9th term = a + 8d
29 = a + 8(29)
29 = a + 232
a = -203
So, the first term (a) is -203 and the common difference (d) is 29 for this arithmetic progression.
Now, let's find the sum of the first 70 terms using the formula for the sum of an AP:
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 total number of terms.
Plugging in the values:
n = 70
a = -203
d = 29
Sn = (70/2)(2(-203) + (70-1)(29))
Sn = (35)(-406 + 69(29))
Sn = (35)(-406 + 2001)
Sn = (35)(1595)
Sn = 55825
Therefore, the sum of the first 70 terms of this arithmetic progression is 55825.