Question

In a arithmetic progression of 50 terms .the sum of first 10 terms is 210 and the sum of last 15 term is 2565 .find the arithmetic progression

Answer 1

Hi there!
Here's the answer:

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Let a be the first term of AP
and d be the common difference

The AP is given as:
a, a+d, a+2d, a+3d, ……… a+49d


Given,
Sum of first 10 terms = 210

a+a+d+a+2d+……+a+9d = 210
=> 10a+45d = 210
=> 2a+9d = 42 ------------(1)

Also Given,
Sum of last 15 terms= 2565

15th term from last = (50 - 15+1) = 36th term from beginning

36th term = a + 35d
{°•° 1st term = a}

Sum of terms in an AP „Sn = n/2[2a+(n-1)d]

=> 15/2[2(a+35d) + 14d] = 2565
=>15[a+35d+7d] = 2565
=> a + 42d = 171 -----------(2)


Do 2×(2) - (1)

2a + 84d = 342
2a + 9d = 42
---------------------
75d = 300
=>d = 4

Substitute in (2)
a + 42d = 171
=> a = 171 - 42(4)
=> a = 171 - 168
=> a = 3

•°• a = 3 & d = 4


•°• The Required AP is :
3, 7, 11, 15, ……………, 199

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Answer 2

Answer:

Step-by-step explanation: ki