Question

Find the sum of the first 70 terms of the arithmetic sequence with first term 14 and common difference 1/2

Answer 1

The sum of the first 70 terms of an arithmetic sequence with first term 14 and common difference 1/2 is 4375/2.

What the sum of the first 70 terms of the arithmetic sequence with first term 14 and common difference 1/2?

Sum of an arithmetic sequence is expressed as;

Sn = n/2 × [2a+(n−1)d]

Given the data in the question;

• First term a₁ = 14
• Common difference d = 1/2
• Number of terms n = 70
• Sum of the first 70 terms S₇₀ = ?

Plug in the given values.

Sn = n/2 × [2a+(n−1)d]

S₇₀ = 70/2 × [2(14) + ( 70 − 1 )1/2]

S₇₀ = 35 × [28 + (69 )1/2]

S₇₀ = 35 × [28 + 69/2]

S₇₀ = 35 × 125/2]

S₇₀ = (35 × 125)/2

S₇₀ = 4375/2

The sum of the first 70 terms of an arithmetic sequence with first term 14 and common difference 1/2 is 4375/2.

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