the 9th and 22nd term of an a.p are 29 and 55 respectively find the sum of its 30 terms.
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Since the 22nd term is 13 terms after the 9th term,
55 = 29 + 13d
Now you can find d and a, and then use your sum formula:
S30 = 30/2 (2a + 29d)
To find the sum of the 30 terms of an arithmetic progression (AP), we need to first find the common difference (d) and the first term (a).
Given that the 9th term is 29 and the 22nd term is 55, we can use these two terms to find the common difference. The formula for finding the nth term of an AP is given by:
nth term = a + (n - 1)d
For the 9th term, we have:
29 = a + 8d
For the 22nd term, we have:
55 = a + 21d
Now, we can solve these two equations to find the values of a and d.
Subtracting the first equation from the second equation, we get:
55 - 29 = (a + 21d) - (a + 8d)
26 = 13d
Dividing both sides by 13, we find:
d = 2
Now, substitute the value of d into either of the above equations. Let's use the first equation:
29 = a + 8 * 2
29 = a + 16
a = 13
So, the first term (a) is 13 and the common difference (d) is 2.
To find the sum of the 30 terms, we can use the formula for the sum of an AP:
Sum of n terms (Sn) = (n/2) * [2a + (n - 1)d]
Substituting the values into the formula, we get:
Sn = (30/2) * [2 * 13 + (30 - 1) * 2]
Sn = 15 * [26 + 29 * 2]
Sn = 15 * (26 + 58)
Sn = 15 * 84
Sn = 1260
Therefore, the sum of the 30 terms of the arithmetic progression is 1260.