Sum of first 7 terms is 63.sum of next 7 terms is 161.find 28th term of AP
Answers
Answer:
57
Explanation:
Sum of first 7 terms =X1+X2+X3+X4+X5+X6+X7
=63
63/7=middle term(X4)
X4=63/7=9
Sum of next 7 terms =X8+X9+X10+X11+X12+X13+X14
=161
161/7=middle term(X11)
X11=161/7=23
we got fourth term=9
eleventh term=23
23-9=7d=14
d=14/7=2
28th term =eleventh term +17d
=23+17×2
=23+34
=57
Hopes that you got my answer☺️
Answer:
Sum of the first n terms of an A.P, Sn = ( n / 2) [ 2a + ( n -1)d ]
Given that sum of the first 7 terms of an A.P is 63 i. e S7 = 63.
⇒ ( 7 / 2) [ 2a + 6d ] = 63
⇒ 2a + 6d = 18 --------(1)
Also given sum of its next 7 terms is 161.
But Sum of first 14 terms = sum of first 7 terms + sum of next 7 terms.
S14 = 63 + 161 = 224
⇒ ( 14 / 2) [ 2a + 13d ] = 224.
⇒ 7 [ 2a + 13d ] = 224.
⇒ [ 2a + 13d ] = 32 -------92)
Solving equ (1) and (2) we obtain
d = 2 and a = 3.
Now t28 = a + ( 28 - 1) d
t28 = 3 + ( 28 - 1) 2
t28 = 57.
∴28th term of this A.P. is 57.