Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
