11. If the gth term of an A.P. is 37 and the 15th
term is 15 more than the 12th term, find the
A.P.
Also, find the sum of first 20 terms of this
A.P.
Answers
Answer:
A.P. : 2,7,12,17......
Sum of first 20 terms in A.P is 990.
Step-by-step explanation:
Given that,
8th term = a+7d = 37 --- equation (1)
To find :
A.P. and sum of first 20 terms in A.P
Solution :
Given that 15th term is 15 more than the 12th term,
a+14d = 15 + a+11d
=> 14d-11d = 15
=> 3d = 15
=> d = 5
Substitute the value of d in 8th term we get,
=> a+7(5) = 37
=> a+35 = 37
=> a = 2
∴ a = 2 , d = 5
Now A.P terms will be:
First term a = 2
Second term : a +d = 7
Third term - a+2d = 12
Fouth term= a+3d = 17 and so on
∴ A.P is 2,7,12,17......
Sum of first 20 terms in
A.P. :
Sn = n/2[2a+(n-1)d]
= 20/2[2x2+(20-1)x5]
= 10[4+19x5]
= 10[4+95]
= 10x99 = 990
∴ Sum of first 20 terms in A.P is 990
Answer:
given, a(9) = 37,. a(15) = 15 + a(12)
to find A.P. and S20
formula used a(n) = a + (n-1)d , Sn = n/2[2a + (n-1)d]
a + 8d = 37 .........(1)
a + 14d = 15 + a + 11d
=> 14d - 11d = 15 [ a cancels out ]
=> 3d = 15
=> d = 5
substituting value of d in equation (1)
a + 8×5 = 37
=> a + 40 = 37
=> a = -3
therefore A.P. a, a + d, a + 2d + .....
=> is -3, -3 +5 , -3 + 2×5 +....
=> -3 , 2, 7, ........... Answer 1st part
now S20 = 20/2 [ 2×(-3) + (20-1)×5 ]
=> 10 [ -6 + 95 ]
=> 10[ 89 ]
=> 890......................Answer 2nd part