Question

If the sum of first 6 terms of an A.P. is 36 and that of the first term is 256 find the sum of the first 10 terms.​

Answer 1

Step-by-step explanation:

Sum of n terms = n/2{2a + (n -1)d }

A/C to question ;

S6 = 6/2{ 2a + (6-1)d }

36 = 3(2a + 5d)

12 = 2a + 5d --------------(1)

again,

S16 = 16/2{ 2a + (16-1)d }

256 = 8{ 2a + 15d }

32 = 2a + 15d --------(2)

solve eqns (1) and (2)

10d = 20

d = 2 put in equation (1)

a = 1

now,

sum of 10th terms = S10 = 10/2{2a +(10-1)d}

= 5{ 2 × 1 + 9 ×2 }

= 5 { 2 + 18}

= 100

hence, sum of first 10terms = 100

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