Question

1+3+5+7+................+89=?​

Answer 1

Hello !!

The question ask for you find the sum of the first 89 natural odd numbers.

In first place you calculate the common difference.

d = (An - Ak)/(n - k)

d = (3 - 1)/(2 - 1)

d = 2/1

d = 2

In second place you calculate how many terms has this sequence.

An = Ak + (n - k) × d

89 = 1 + (n - 1) × 2

89 = 1 + 2n - 2

89 = 2n - 2 + 1

89 = 2n - 1

2n - 1 = 89

2n = 89 + 1

2n = 90

n = 90/2

n = 45

In third place you calculate the sum.

Sn = (n/2) × [2Ak + (n - k) × d]

S45 = (45/2) × [2(1) + (45 - 1) × 2]

S45 = 22.5 × [2 + 44 × 2]

S45 = 22.5 × [2 + 88]

S45 = 22.5 × 90

S45 = 2025

Final result : 2025 is the sum.

I hope I have collaborated !

Answer 2

Eso vino en mi tarea espero te sirva xd