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Pavel [41]
3 years ago
12

Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.

Mathematics
1 answer:
Sholpan [36]3 years ago
8 0

The first five terms of the sequence are -10, -33, -125, -493, -1965

Explanation:

The given expression is a_n=4a_{n-1}+7

And a_1=-10 is the first term of the sequence.

We need to determine the first five terms of the sequence.

<u>Second term:</u>

Substituting n = 2 in the expression a_n=4a_{n-1}+7, we have,

a_2=4a_{2-1}+7

a_2=4a_1+7

a_2=4(-10)+7

a_2=-40+7=-33

Thus, the second term is -33

<u>Third term:</u>

Substituting n = 3 in the expression a_n=4a_{n-1}+7, we have,

a_3=4a_2+7

a_3=4(-33)+7

a_3=132+7=-125

Thus, the third term is -125

<u>Fourth term</u><u>:</u>

Substituting n = 4 in the expression a_n=4a_{n-1}+7, we have,

a_4=4a_3+7

a_4=4(-125)+7

a_4=-500+7=-493

Thus, the fourth term is -493

<u>Fifth term</u>:

Substituting n = 5 in the expression a_n=4a_{n-1}+7, we have,

a_5=4a_4+7

a_5=4(-493)+7

a_5=-1972+7=-1965

Thus, the fifth term is -1965

Hence, the first five terms of the sequence are -10, -33, -125, -493, -1965

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