If the first term of an AP is -5 and the common difference is 2, then the sum of the first 6 terms is
a. 0
b. 5
c. 6
d. 15

Solution:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.

From the question:

a = -5

d = 2.

The formula to find the sum is

Sn = n/2 [2a + (n - 1)d].

Substituting the values, we get,

S₆ = 6/2 [2a + (6 - 1)d]

S₆ = 3[2(-5) + 5(2)]

S₆ = 3(-10 + 10)

S₆ = 3(0)

S₆ = 0.

Therefore, S₆ = 0.

✦ Try This: How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

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NCERT Exemplar Class 10 Maths Exercise 5.1 Problem 15

If the first term of an AP is -5 and the common difference is 2, then the sum of the first 6 terms is, a. 0, b. 5, c. 6, d. 15

Summary:

If the first term of an AP is -5 and the common difference is 2, then the sum of the first 6 terms is 0

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☛ Related Questions:

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• In an AP if a = 1, aₙ = 20 and Sₙ = 399, then n is, a. 19, b. 21, c. 38, d. 42
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