The 6th term of an ap -5 and the 10th term is 21 find the sum of the first 30th term. i need with a solving

1702.5

Step-by-step explanation:

The n th term of an arithmetic progression is

= a + (n - 1)d

where a is the first term and d the common difference, hence

a + 5d = - 5 → (1) and

a + 9d = 21 → (2)

Subtract (1) from (2) term by term

4d = 26 ( divide both sides by 4 )

d = = 6.5 ← common difference

Substitute d = 6.5 into (1 )

a + 32.5 = - 5 ( subtract 32.5 from both sides )

a = - 37.5 ← first term

The sum to n terms of an arithmetic progression is

= [ 2a + (n - 1)d ], hence

= 15 [ - 75 + (29 × 6.5) ]

                          = 15 [ - 75 + 188.5 ]

                          = 15 × 113.5

                          = 1702.5