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2 years ago

Two terms of an arithmetic sequence are a10=16 and a35=66 find the sum of the first 75 terms

1 answer:

4 0

The sum of the first 75 terms of the arithmetic sequence that has 10th term as 16 and the 35th term as 66 is 5400.

<h3>How to find the sum of terms using Arithmetic sequence formula</h3>

aₙ = a + (n - 1)d

where

a = first term

d = common difference

n = number of terms

Therefore, let's find a and d

a₁₀ = a + (10 - 1)d

a₃₅ = a + (35 - 1)d

Hence,

16 = a + 9d

66 = a + 34d

25d = 50

d = 50 / 25

d = 2

16 - 9(2) = a

a = 16 - 18

a = -2

Therefore, let's find the sum of 75 terms of the arithmetic sequence

Sₙ = n / 2 (2a + (n - 1)d)

S₇₅ = 75 / 2 (2(-2) + (75 - 1)2)

S₇₅ = 37.5 (-4 + 148)

S₇₅ = 37.5(144)

S₇₅ = 5400

learn more on arithmetic sequence here: brainly.com/question/1687271

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