We know that the 10th term of the arithmetic progression is -5 and the 15th term is -7.
Using the formula for the nth term of an arithmetic progression, we can write the equations:
a + 9d = -5 ...(1)
a + 14d = -7 ...(2)
where a is the first term and d is the common difference.
Subtracting equation (1) from equation (2), we get:
( a + 14d ) - ( a + 9d ) = -7 -(-5)
5d = -2
d = -2/5
Substituting the value of d in equation (1), we get:
a + 9(-2/5) = -5
a - 18/5 = -5
a = -5 + 18/5
a = -25/5 + 18/5
a = ( -25 + 18 ) / 5
a = -7/5
So, the first term (a) is -7/5 and the common difference (d) is -2/5.
The formula for the sum of the first n terms of an arithmetic progression is given by:
S_n = n/2(2a + (n-1)d)
Substituting the values, we have:
S_20 = 20/2(2(-7/5) + (20-1)(-2/5))
= 10(-14/5 + 19(-2/5))
= 10(-14/5 + (-38/5))
= 10(-14 - 38)/5
= 10(-52)/5
= -520/5
= -104
Therefore, the sum of the first 20 terms is -104. Answer: \boxed{-104}.
The 10th and 15th terms of an a.p are -5 and -7 and the half, respectively. What is the sum of the first 20 terms
1 answer