Question

the common difference in an arithmetic sequence is 8. if the sum of the first 10 terms is 56, find the first term of the sequence

Answer 1

Answer:

the first term

a₁ = -30.4

Step-by-step explanation:

Let (an) be an arithmetic sequence with a common difference 8.

a₁ represents its first term.

And let S be the sum of the first 10 terms of the sequence.

Then

S = a₁ + a₂ + ………+ a₁₀

a₁₀ = a₁ + 8(10 - 1) = a₁ + 8×9 = a₁ + 72

S = a₁ + a₂ + ………+ a₁₀

  $=\frac{10}{2} \times \left( a_{1}+a_{10}\right)$

  $=5} \times \left( a_{1}+(a_{1}+72)\right)$

  $=5} \times \left( 2a_{1}+72\right)$

  $=10a_{1}+360$

We are given :  S = 56

then

56 = 10a₁ + 360

then

-10a₁ = 360 - 56

then

-10a₁ = 304

then

a₁ = -304/10

   = -30.4