Question

In a A.p sum of first three terms is 15 and sum of next three is 42. Then find sum of first 10 terms of the A.P.

Answer 1

Answer:

S10 = 155

Step-by-step explanation:

S3 = 3/2 [2a + 2d]

= 15 = 3/2 × 2[a + d]

= 15 = 3[a + d] =》 a + d = 15/3 =》 a + d = 5

= d = 5 - a

Now, S6 - S3 = 42

= 6/2 [2a + 5d] - 15 = 42

= 3[2a + 5d] = 42 + 15

= 6a + 15d = 57 =》 6a + 15(5 - a) = 57

= 6a + 75 - 15a = 57

= 15a - 6a = 75 - 57 =》9a = 18

=》 a = 18/9 =》 a = 2

Now, d = 5 - 2 =》 d = 3

Now, S10 = 10/2 [2×2 + 9×3]

= 5[4 + 27] =》 5[31] =》 155

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