Question

the sum of the first and fifth of an a.p is 30 and the sum of fourth and eight term of the same a.p is 46 .find the sum of first 10 term of this a.p​

Answer 1

Answer:

216 2/3

Step-by-step explanation:

Given AP: a₁+a₅=30, a₄+a₈=46, S₁₀=?

Formulas to be used: aₙ=a₁+(n-1)d, Sₙ=(a₁+aₙ)n/2

1) a₁+a₅=2a₁+4d =30 => a₁+2d=15

2) a₄+a₈=2a₁+10d =46 => a₁+5d=23

From above 2 equations we get

a₁+5d- a₁-2d= 23-15

d=8/3

a₁+16/3=15 =>

a₁=29/3

Now, having the values of the first term and common difference we can find the sum of first 10 terms:

S₁₀=(a₁+a₁₀)*10/2=5*(2a₁+9d)=5*(58+72)/3=650/3=216 2/3