Let a 1 ,   a 2 ,   … ,   a 30 be an A.P., S =   ∑ i = 1 30 a i and T =   ∑ i = 1 15 a ( 2 i - 1 ) . If a 5 = 27 and S - 2 T = 75 , then a 10 is equal to:

Question

Let a 1 , &#160; a 2 , &#160; &#8230; , &#160; a 30 be an A.P., S = &#160; &#8721; i = 1 30 a i and T = &#160; &#8721; i = 1 15 a ( 2 i - 1 ) . If a 5 = 27 and S - 2 T = 75 , then a 10 is equal to:

Aicharya · Accepted Answer

Let common difference = d &#8756; S = &#160; &#8721; i = 1 30 a i = 30 2 2 a 1 + 29 &#160; d &#8756; S = 15 &#160; 2 a 1 + 29 &#160; d . . . . . . . . &#160; ( i ) T = 15 2 2 a 1 + 14 &#160; . &#160; 2 d T = 15 &#160; a 1 + 14 d &#160; . . . . . . . . . . . ( i i ) a 1 + 4 d = 27 . . . . . . . . . &#160; ( i i i ) S - 2 T = 75 &#8658; 15 2 a 1 + 29 &#160; d - 30 &#160; a 1 + 14 d &#160; = 75 &#8658; 15 &#160; d 29 - 28 = &#160; 75 &#8658; d = 5 &#8756; &#160; from ( i i i ) a 1 = 7 &#8756; &#160; a 10 = a 1 + 9 d = 7 + 45 = 52

Let a 1 ,   a 2 ,   … ,   a 30 be an A.P., S =   ∑ i = 1 30 a i and T =…

Solution

Let a 1 , &#160; a 2 , &#160; &#8230; , &#160; a 30 be an A.P., S = &#160; &#8721; i = 1 30 a i and T =…

Solution

Let a 1 , a 2 , … , a 30 be an A.P., S = ∑ i = 1 30 a i and T =…