# Geometric Progression Worksheet

This worksheet may help you to know about the Geometric Progression. In Geometric Progression each term bears a constant ratio with its preceding term. This constant ratio is called as ratio of the geometrical progression. In Geometrical Progression let a is the first term & r is the common ratio. The general expression of the Geometrical Progression is
a,ar,ar2,ar3,ar4, ......

Geometric Progression Formula:
The nth term of the G.P is given by,
Tn = a x rn - 1
Sum of n terms is,
Sn = a x (rn - 1) / (r - 1)

Geometric Progression Examples:
Example 1
How many terms are there in 2,4,8,16, ....,512.

Solution:
Here a = 2 & r = 4/2 = 2.
Tn = a x rn - 1
512 = 2 x 2n-1
2n - 1 = 256 = 28
n - 1 = 8
n = 9

Example 2
Find the value of 3 + 32 + 33 + 34 + .... + 312 = ?
Solution:
Here a = 3 & r = 3 , n = 12
Sn = a x (rn - 1) / (r - 1)
= 3 x (312 - 1) / (3 - 1)
= 3 x 531440 / 2
= 1594320 / 2
= 797160
Hence the required Sum is 797160.
{"ft_lang_label":"__label__en","ft_lang_prob":0.81547254,"math_prob":0.99996626,"size":930,"snap":"2020-34-2020-40","text_gpt3_token_len":345,"char_repetition_ratio":0.16306695,"word_repetition_ratio":0.103286386,"special_character_ratio":0.4311828,"punctuation_ratio":0.18181819,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999472,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-22T07:14:14Z\",\"WARC-Record-ID\":\"<urn:uuid:bbb910c0-8c98-4bba-aed6-2bc110ec14b9>\",\"Content-Length\":\"21773\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d730a092-63d5-4a3b-ae6f-919786842b57>\",\"WARC-Concurrent-To\":\"<urn:uuid:39732c59-75ce-48ed-96ad-76ed6a60af5c>\",\"WARC-IP-Address\":\"167.114.48.73\",\"WARC-Target-URI\":\"https://ncalculators.com/math-worksheets/geometric-progression-worksheet.htm\",\"WARC-Payload-Digest\":\"sha1:2KU24OFRR3427TQMGIWLKWOP6HDNKWW2\",\"WARC-Block-Digest\":\"sha1:SSJUXNNPXX4QZDDQNGBKFJQFHJH4VRG7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400204410.37_warc_CC-MAIN-20200922063158-20200922093158-00245.warc.gz\"}"}