Question

the sum of first 7 term of an A.P is 49' and that of 17 terms is 289'find the sum of first 25 terms​

Answer 1

Answer:

625

Step-by-step explanation:

Sₙ = n/2(2a + (n-1)d]

S₇ = 7/2(2a + 6d) = 49 => a + 3d = 7 --------------> [1]

S₁₇ = 17/2(2a +16d )= 289 => a+8d = 17------------> [2]

Solve [1] and [2]

a + 8d = 17

a + 3d =   7

-  -          -

-----------------------

5d = 10

=> d = 2

Substitute value of d = 2 in [1]

a + 3d = 7 => a = 1

S₂₅ = 25/2(2 + 24*2) = 25/2(50) = 625.