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Varvara68 [4.7K]
3 years ago
5

Find the sum of the first 12 terms of the sequence. 1, -4, -9, -14, . . . (2 points)

Mathematics
2 answers:
egoroff_w [7]3 years ago
8 0

Answer:

sum of the first 12 terms of the sequence. 1, -4, -9, -14, . . = -318

Step-by-step explanation:

The given AP is,

1, -4, -9, -14, . . .

first term a = 1,

common difference d = -4 - 1 = -5

number of terms  n = 12

<u>Equation:</u>

Sum of n terms of AP, S₁₂ = n/2[2a + (n - 1)d]

S₁₂ = 12/2[(2*1) + (12 - 1)*(-5)]

S₁₂ = 6[2 + (11*(-5))]

S₁₂ = 6[2 - 55] = 6*(-53) = -318

Therefore sum of the first 12 terms of the sequence. 1, -4, -9, -14, . . = -318

omeli [17]3 years ago
5 0

Answer:

The sum of first 12 terms of the sequence. 1, -4, -9, -14, . .  is -318.

Step-by-step explanation:

Given sequence  1, -4, -9, -14, . . .

We have to find the sum of first 12 terms of the sequence. 1, -4, -9, -14, . .

Consider  the given sequence 1, -4, -9, -14, . . .

a_1=1 ,a_2=-4,a_3=-9

First calculate the common difference (d)

a_2-a_1=-4-1=-5\\a_3-a_2=-9+4=-5

Thus, common difference is -5

We know sum of terms in an Arithmetic progression is given by,

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

where n is number of terms ,

a = first term

d = common difference

Here, n = 12 , a= 1 , d = -5

S_{12}=\frac{12}{2}(2(1)+(12-1)(-5))

Solving , we get,

S_{12}=6(2+11(-5))

S_{12}=6(2-55)

S_{12}=6(-53)

S_{12}=-318

Thus, the sum of first 12 terms of the sequence. 1, -4, -9, -14, . .  is -318.

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