Question

Determine the number of terms in the sequence: –45, –32, –19, –6, ..., 124.

Answer 1

The number of terms in the sequence: –45, –32, –19, –6, ..., 124 = 9.

The common difference is -45 - (-32)= 13

                                                  d = 13.

What is arithmetic progress?

AP is a sequence of numbers in order, in which the difference among any two consecutive numbers is a constant cost. it's also referred to as mathematics series.

using arithmetic progress:-

last term = (n-1)d

first term(a) = –45

    term = a + (n-1)d

there is a difference of 13, so the sequence will be

–45, –32, –19, –6,7, 20, 33, 46, 59, 72, 85, 98, 111, 124.

∴ number of terms = 9

Learn more about arithmetic sequence here:-brainly.com/question/6561461

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Answer 2

Step-by-step explanation:

$- 32 + 45 = 13 \\ t_{n} = ( a_{1} + (n - 1)d) \\ \\ d = 13 \: \: a_{1} = - 45$

$t_{n} = - 45 + (n - 1)13 = = = > \\ - 45 + 13n - 13 = = = > \\ t_{n} = 13n - 58$

and now

$124 = 13n - 58 = = = > \\ 182 = 13n = = = > n = 14$