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AP ICET 2015 Paper

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Question : 4 of 200

Marks: +1, -0

What is the sum of the first 20 terms of the Arithmetic Progression ?

I. The sum of the first term and 20th term of the AP is 120.

II. The common difference of the AP is 5.

if the statement I alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Solution:

Given: Terms are in A.P

No. of terms, n = 20

The sum of first n terms of an A.P is given by

S_n = \frac{n}{2} = (\text{First term} + \text{last term})

or

S_n = \frac{n}{2}[2a + (n-1)d]

where

a: first term

d: common difference

I. Given:First term + 20th term=120

20th term is the last term.

n = 20

\Rightarrow S_{20} = \frac{20}{2} \times 120 = 1200

∴ Ι alone is sufficient.

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