Advertisements
Advertisements
प्रश्न
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
विकल्प
87
88
89
90
Advertisements
उत्तर
89
\[a_7 = 34\]
\[ \Rightarrow a + 6d = 34 . . . . . \left( 1 \right)\]
\[\text { Also,} a_{13} = 64\]
\[ \Rightarrow a + 12d = 64 . . . . . \left( 2 \right)\]
Solving equations
\[\left( 1 \right) \text { and } \left( 2 \right)\], we get:
a = 4 and d = 5
\[\therefore a_{18} = a + 17d\]
\[ = 4 + 17\left( 5 \right)\]
\[ = 89\]
APPEARS IN
संबंधित प्रश्न
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
3, −1, −5, −9 ...
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Find:
10th term of the A.P. 1, 4, 7, 10, ...
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
Is 302 a term of the A.P. 3, 8, 13, ...?
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
Find the sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?
We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
Mark the correct alternative in the following question:
If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is
If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the A.P., then Sq equals ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
