Find the sums given below :
(iii) –5 + (–8) + (–11) + . . . + (–230)

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

In an AP:
(vii) given $a = 8, a_n = 62, S_n = 210$, find $n$ and $d$.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first $n$ terms.

Find the sums given below :
(ii) 34 + 32 + 30 + . . . + 10

200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Fig. 5.5). In how many rows are the 200 logs placed and how many logs are in the top row?

Find the sum of the first 15 multiples of 8.

In an AP:
(v) given $d = 5, S_9 = 75$, find $a$ and $a_9$.

Find the sum of the odd numbers between 0 and 50.

A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $\pi = \frac{22}{7}$) [Hint : Length of successive semicircles is $l_1, l_2, l_3, l_4, . . .$ with centres at A, B, A, B, . . ., respectively.]

In an AP:
(vi) given $a = 2, d = 8, S_n = 90$, find $n$ and $a_n$.

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

If the sum of the first $n$ terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the $n$th terms.

Find the sums given below :
(i) $7 + 10\frac{1}{2} + 14 + . . . + 84$

In an AP:
(iii) given $a_{12} = 37, d = 3$, find $a$ and $S_{12}$.

Find the sum of first 22 terms of an AP in which $d = 7$ and 22nd term is 149.

Show that $a_1, a_2, . . ., a_n, . . .$ form an AP where $a_n$ is defined as below :
(ii) $a_n = 9 – 5n$
Also find the sum of the first 15 terms in each case.

Show that $a_1, a_2, . . ., a_n, . . .$ form an AP where $a_n$ is defined as below :
(i) $a_n = 3 + 4n$
Also find the sum of the first 15 terms in each case.

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

In an AP:
(iv) given $a_3 = 15, S_{10} = 125$, find $d$ and $a_{10}$.