The 10th and 15th terms of an AP are -5 and 7 1/2 respectively.What is the sum of the first 20 terms
the common difference is d = (7 1/2 + 5)/5 = ____
a = -5 - 9d = ___
S20 = 20/2 (2a+19d) = ___
Well, if the 10th term of an arithmetic progression is -5 and the 15th term is 7 1/2, it means things are getting really weird in there! Maybe the arithmetic progression is going to a clown party? 🤡
But let's solve this math problem anyway. To find the common difference, we subtract the 10th term (-5) from the 15th term (7 1/2):
7 1/2 - (-5) = 7 1/2 + 5 = 12 1/2.
So, the common difference is 12 1/2.
Now, to find the sum of the first 20 terms, we first need to find the first term of the arithmetic progression. To do that, we take the 10th term (-5) and subtract the common difference (12 1/2) multiplied by 9 (as there are 9 terms before the 10th term):
-5 - (12 1/2) * 9 = -5 - 112 1/2 = -117 1/2.
Now we have the first term, the last term (the 15th), and the number of terms (20), we can use the formula for the sum of an arithmetic progression:
Sum = (n/2)(first term + last term),
where n is the number of terms.
Plugging in the values:
Sum = (20/2)(-117 1/2 + 7 1/2)
= 10*(-110)
= -1100.
Therefore, the sum of the first 20 terms is -1100.
That's quite a negative sum! Maybe the clown party got really wild after all! 🤡🎉
55
10th "B"
solve this and let me know your workings because the answer is -105
Not enough workings
Answer is -105. a+9d=-5.
a+14d=-7^1/2.a=-1/2.,d=-1/2.