Question

in an AP the sum of first 10 terms is 155 while the sum of next 5 terms is 190 find the sixth term​

Answer 1

Answer:

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

S10 = (10/2)[2a+(10-1)d] = 155

5[2a+9d] = 155

2a+9d = 31 ------(1)

S15-S10 = 190

S15 = 190+S10 = 190+155 =345

S15 = (15/2)[2a + (15-1) d]

345 = (15/2) [2a + 14d]

23*2 = 2a+14d

46 = 2a+14d-------(2)

(2) - (1) ;

2a + 14d = 46

2a + 9d = 31

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

5d = 15

d = 15/5 = 3

put d= 3 in (1)

9(3) + 2a = 31

27 + 2a = 31

2a = 31-27 = 4

a = 4/2

a = 2

a = 2; d = 3

an = a+(n-1) d

a6 = 2+(6-1) 3

a6 = 2+15 = 17

a6 = 17

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