Question

In an arithmetic progression the sum of the first ten terms is 400 and the sum of the next ten terms is 1000 find the common difference and the first term

Answer 1

Answer:

a=13,d=6

Step-by-step explanation:

The Explanation is provided in the attachment

Answer 2

Dear friend,

● Answer -

Common difference = 6

First term = 13

● Explanation -

Let a and d be first term and common difference for the AP.

Sum of first 10 terms is calculated as -

S10 = n/2 [2a + (n-1)d]

S10 = 10/2 [2a + (10-1)d]

400 = 5 (2a + 9d)

400 = 10a + 45d ...(1)

Sum of next 10 terms is calculated as -

S20-S10 = 20/2 [2a + (20-1)d] - 10/2 [2a + (10-1)d]

S20-S10 = 10 (2a + 19d) - 5 (2a + 9d)

1000 = 20a + 190d - 10a - 45d

1000 = 10a + 145d ...(2)

Substracting (2) from (1),

1000 - 400 = (10a + 145d) - (10a + 45d)

600 = 100d

d = 600/100

d = 6

Putting this in (1),

400 = 10a + 45×6

400 = 10a + 360

10a = 400 - 270

a = 130 / 10

a = 13

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