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erma4kov [3.2K]
3 years ago
12

Identify the 12th term of the arithmetic sequence in which a7 = 40 and a18 = 106.

Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

we are given

airthematic sequence

we can use nth term formula

a_n=a_1+(n-1)d

n is number of terms

an is nth term

d is common difference

a1 is first term

We are given

a7=40

we can use it

a_7=a_1+(7-1)d

40=a_1+6d

a_1+6d=40

a18 = 106

a_1_8=a_1+(18-1)d

a_1+17d=106

we can subtract both equations

a_1+17d-a_1-6d=106-40

11d=66

d=6

now, we can find a1

a_1+6d=40

we can plug d=6

a_1+6*6=40

a_1=4

12th term:

a_1_2=a_1+(12-1)d

now, we can plug values

a_1_2=4+(12-1)*6

a_1_2=4+66

a_1_2=70

so, 12th term is 70...........Answer

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Hello!

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