I need help on this problem please.

Question

For an arithmetic sequence, . If the common difference is -5, find:

a1=_______

the sum of the first 48 terms =________

Answer 1

Use the explicit formula for an arithmetic sequence:

a_n = a₁ + d·(n-1)

We are given a₁₆ = 88 and d = -5:

a_n = a₁ + d·(n-1)

88 = a₁ + (-5)·(16-1)

Solve for a₁. To find the sum of the first 45 terms, use the sum formula for n = 45:

S = n(a₁+a_n)/2

You just found the value of a₁ above. To find a₄₅, use the explicit formula above given that you now know a₁, d, and n (=45)

a₄₅ = a₁ + (-5)(45-1) = ?