Question

find the sum of first 30 terms of the ap whisw 5 term is 13 and 8 term is 19​

Answer 1

Answer:

sum of 30 terms of an AP= 170.

Answer 2

Solution:-

:- Given

=> T₅ = 13

=> T₈=19

To Find

=> The sum 30 term ( S₃₀)

Formula

=> Tₙ = a + ( n - 1 )d

Now

For T₅

=> 13 = a + ( 5 - 1 )d

=> 13 = a + 4d ....(i)eq

For T₈

=> 19 = a + ( 8 - 1 )d

=> 19 = a + 7d ....(ii)eq

Now subtract (ii) from (i)

=> a + 4d - a - 7d = 13 - 19

=> - 3d = - 6

=> d = 2

Now put the value of d on (i) eq

=> 13 = a + 4d

=> 13 = a + 4 × 2

=> 13 = a + 8

=> a = 13 - 8

=> a = 5

Now we have to find S₃₀ term

:- Formula

=> Sₙ = n/2 {2a + ( n - 1 )d}

:- a = 5 , d = 2 and n = 30

=> S₃₀ = 30/2{2×5 + ( 30 - 1 )2}

=>S₃₀ = 15 { 10 + 29 × 2 }

=> S₃₀ = 15{ 10 + 58 }

=> S₃₀ = 15{ 68 }

=> S₃₀ = 1020

Sum of 30 term is 1020