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Anna007 [38]
3 years ago
7

The common difference of an ap is -2 find its sum of first term is hundred and last term is -10 with full solution

Mathematics
1 answer:
mixer [17]3 years ago
4 0

Answer:

2520

Step-by-step explanation:

The n th term of an AP is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference.

To find the number of terms given a_{n} = - 10 , d = - 2 and a₁ = 100, then

100 - 2(n - 1) = - 10 ( subtract 100 from both sides )

- 2(n - 1) = - 110 ( divide both sides by - 2 )

n - 1 = 55 ( add 1 to both sides )

n = 56 ← number of terms

Given n, a₁ and a₅₆ , then the sun of the terms is

S_{56} = \frac{n}{2} (a₁ + a₅₆ )

      = \frac{56}{2} (100 - 10) = 28 × 90 = 2520

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