The first term of an ap is -5 and the last term is 45. If the sum of the terms of ap is 120 then find the number of terms and the common difference
Answers
Step-by-step explanation:
If the sum of the terms of the AP is 120, then find the number of terms and the common difference. Last term of an AP, l = 45. ... Therefore, the number of terms is 6 and the common difference is 10
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Given, the first term of an AP, a = -5
Last term of an AP, l = 45.
Sum of the term of the AP, S = 120
We have to find the number of terms and the common difference.
We know that, if l is the last term of an AP, then the sum of the terms is given by
S = n/2[a+l]
So, 120 = n/2[-5+45]
120 = n/2[40]
120 = 20n
n = 120/20
n = 6
The nth term of an AP is given by
aₙ = a + (n - 1)d
Given, a₆ = 45
45 = -5 + (6 - 1)d
45 + 5 = 5d
50 = 5d
d = 50/5
d = 10
Therefore, the number of terms is 6 and the common difference is 10.
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