The first term of an arithmetic progress is -10 and the last term is 35. if the common difference is 3, find the number of the terms in the sequence

Question

The first term of an arithmetic progress is -10 and the last term is 35. if the common difference is 3, find the number of the terms in the sequence. (B) calculate the sum of all the terms

Answer 1

The explicit formula for an arithmetic sequence is

a_n= a₁ + d(n-1)

Where a₁ is the first term, d is the common difference, n is the number of terms

we can plug in all the given info to calculate the n

35= -10+3(n-1)

Add 10 to both sides

45=3(n-1)

Divide both sides by 3

15=n-1

Add 1 to both sides

n=16

There are 16 terms in the sequence

B) sum is found with this formula

S_n =(n/2)(a₁+a_n)

n is the number of terms

a₁ is first term

a_n is last term

S_n = (16/2)(-10+35)=(8)(25)=200