Find the sum of the first 10 terms of the arithmetic sequence

Question

a₄ = 26

a₉ = 56

Answer 1

Use following formulas

a_{n =} a +(n-1)d nth term of arithmetic sequence

S =n/2(2a +(n-1)d) sum of arithmetic sequence

n =10, find a and d with help of following equation below

a₄ = a +(4-1)d = 26

a₉ = a +(9-1)d = 56

or

a +3d = 26

a + 8d = 56

Hope these guidelines help

Answer 2

S_n=n/2(a₁+a_n)

First, we can find d

d = (56-26)/(9-4)

d=30/5

d=6

Now, we can find a₁

a_n = a₁ + (n-1)d

56=a₁ + (9-1)6

56=a₁ + 48 Subtract 48 from both sides

8=a₁

Now we can find a₁₀

a₁₀ = 8 + (10-1)6

a₁₀ = 8 + 54

a₁₀ = 62

Finally we have everything we need for the sum formula

S_n=n/2(a₁+a_n)

S₁₀=10/2(8+62)

S₁₀=5(70)

S₁₀=350