the first and last Terms of AP are a and l respectively . show that the sum of the nth term from the beginning and the nth term from the end is (a+l).
Answers
Answer:
Given : First term of the AP = a
Given : Last term of the AP = l.
Given : Total number of terms = n.
Common difference from the beginning = d.
Common difference from the end = -d.
∴ Last term of the AP = nth term of the AP
⇒ an = l
⇒ a + (n - 1) * d = l
Now,
⇒ nth term of the AP from the beginning an = a + (n - 1) * d
⇒ nth term from the end = l + (n - 1) * (-d)
= l - (n - 1) * d
Sum of nth term from the beginning + nth term from the end is given by:
⇒ a + (n - 1) * d + [l - (n - 1) * d]
⇒ a + (n - 1) * d + l - (n - 1) * d
⇒ a + nd - d + l - nd + d
⇒ a + l.
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Step-by-step explanation:
Given : First term of the AP = a
Given : Last term of the AP = l.
Given : Total number of terms = n.
Common difference from the beginning = d.
Common difference from the end = -d.
∴ Last term of the AP = nth term of the AP
⇒ an = l
⇒ a + (n - 1) * d = l
Now,
⇒ nth term of the AP from the beginning an = a + (n - 1) * d
⇒ nth term from the end = l + (n - 1) * (-d)
= l - (n - 1) * d
Sum of nth term from the beginning + nth term from the end is given by:
⇒ a + (n - 1) * d + [l - (n - 1) * d]
⇒ a + (n - 1) * d + l - (n - 1) * d
⇒ a + nd - d + l - nd + d
⇒ a + l.
Hope this helps!
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