Advertisements
Advertisements
Questions
The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.
The 4th term of an A.P. is 22, and the 15th term is 66. Find the sum of its 8 terms.
Advertisements
Solution
Let a be the first term and d be the common difference of the given A.P.
Now,
4th term = 22
⇒ a + 3d = 22 ...(i)
15th term = 66
⇒ a + 14d
= 66
Subtracting (i) from (ii), we have
11d = 44
⇒ d = 4
Substituting the value of d in (1), we get
a = 22 − 3 × 4
= 22 − 12
=10
⇒ First term = 10
Now
Sum of 8 terms = `8/2[2xx10+7xx4]`
= 4[20 + 28]
= 4 × 48
= 192
APPEARS IN
RELATED QUESTIONS
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
2x2 - (3k + 1)x - k + 7 = 0.
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
(x2 + 1)2 – x2 = 0 has ______.
